Analysis of the Mass and Potential Energy of World Trade Center

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Analysis of the Mass and Potential Energy of World Trade Center
Analysis of the Mass and Potential Energy
of World Trade Center Tower 1
Gregory H. Urich
B.S. Electrical and Computer Engineering
1
Abstract
The mass and potential energy of one of the Twin Towers is calculated based on available
data. The mass for each floor is established based on floor types, documented design
loads, and estimated in-service live loads. The calculated mass of 288,100 metric tons
(317,500 short tons) is found to correspond with two other comparable structures in
terms of mass per unit floor area, NIST’s SAP2000 model, and the reported amount of
recovered debris. The calculated mass refutes the popular notion that the building
weighed 500,000 tons.
2
Table of Contents
Please note: For ease of navigation, each entry in the table of contents is hyperlinked to
the corresponding section in the document. Simply click on an entry in the table of
contents to navigate to that section.
1
2
3
Abstract.......................................................................................................... 1
Table of Contents ............................................................................................. 1
Introduction .................................................................................................... 3
3.1
Popular numbers ....................................................................................... 4
3.2
General overview of design and construction ................................................ 5
3.3
Original design.......................................................................................... 5
3.4
Amount of steel ........................................................................................ 6
3.5
NIST reference models............................................................................... 6
3.6
NIST’s “Tower and Aircraft Impact Models” ................................................... 7
4 Method ........................................................................................................... 8
4.1
Floor Areas ............................................................................................... 8
4.2
Floor Types..............................................................................................10
4.2.1
Normal Floors ....................................................................................10
4.2.2
Mechanical floors................................................................................11
4.2.3
Sublevels ..........................................................................................11
4.2.4
Special floors .....................................................................................11
4.3
Gravity Loads ..........................................................................................11
4.3.1
Foundation ........................................................................................11
4.3.2
Amount of Core Column Steel ..............................................................12
4.3.3
Variation of Core Column Steel ............................................................12
4.3.4
Amount of External Column Steel .........................................................13
4.3.5
Variation of External Column Steel .......................................................13
4.3.5.1
Above Floor 9 ..............................................................................13
4.3.6
Gravity Loads for Normal Floors ...........................................................14
4.3.6.1
CDLs inside the Core (normal floors) ..............................................14
4.3.6.2
SDLs Inside the Core (normal floors) ..............................................15
4.3.6.3
SLLs inside the core (normal floors) ...............................................16
4.3.6.4
CDLs outside the Core (normal truss-framed floors) .........................16
4.3.6.5
SDLs outside the Core (normal truss-framed floors) .........................17
1
5
6
7
8
4.3.6.6
SLLs outside the Core (normal truss-framed floors) ..........................17
4.3.7
Gravity Loads for Mechanical Floors ......................................................17
4.3.7.1
CDLs inside the Core (mechanical floors) ........................................17
4.3.7.2
SDLs inside the Core (mechanical) .................................................18
4.3.7.3
SLLs inside the core (mechanical floors)..........................................19
4.3.7.4
CDLs outside the Core (mechanical beam-framed floors)...................20
4.3.7.5
SDLs outside the Core (mechanical beam-framed floors)...................20
4.3.7.6
SLLs outside the Core (mechanical beam-framed floors) ...................20
4.3.8
Gravity Loads for Sublevels .................................................................20
4.3.9
Gravity Loads for Special Floors ...........................................................21
4.3.10 Hat Truss ..........................................................................................21
4.3.11 Aluminum cladding and elevators .........................................................22
Results ..........................................................................................................23
5.1
Summary of Results .................................................................................23
5.2
Detailed Results .......................................................................................23
Discussion......................................................................................................25
6.1
Comparison with Other Buildings................................................................25
6.2
Comparison to Values Extracted from SAP2000 model ..................................25
6.2.1
Comparison to CDL from SAP2000 Model ..............................................26
6.2.2
Comparison to SDL from SAP2000 Model ..............................................26
6.2.3
Comparison to Live Loads from SAP2000 Model .....................................26
6.3
Comparison to Total Column Loads in NIST Models .......................................27
6.4
Comparison to Amount of Debris Removed from Ground Zero........................27
6.4.1
The Amount of Debris .........................................................................27
6.4.2
Calculation of Debris Amount ...............................................................27
6.4.3
Comparison of Calculated Mass to Recovered Mass .................................27
6.4.4
Conclusions .......................................................................................28
References .....................................................................................................29
Appendices ....................................................................................................31
8.1
Appendix 1: Calculation of Debris Amount ...................................................31
8.1.1
Comments on Calculation of Debris Mass ..............................................33
8.2
Appendix 2: Calculation of Rolled Core Column Mass ....................................34
8.3
Appendix 3: Core Column Data for Selected Floors .......................................35
2
3
Introduction
In the aftermath of the World Trade Center Disaster, the Federal Emergency
Management Agency (FEMA) and the National Institute of Standards and Technology
(NIST) conducted investigations of considerable scope regarding building performance
and the collapse of the World Trade Center Towers. The FEMA report described a
pancake-type progressive floor collapse scenario causing the removal of lateral support
on several floors leading to buckling in unshored columns which were weakened by fire
and partially damaged by aircraft impact.3 The FEMA report was not rigorous and the
conclusions regarding collapse initiation and progressive collapse can only be considered
to be an educated guess by the investigators. The more rigorous NIST reports described
aircraft impact damage and collapse initiation based on forensic evidence and computer
simulations. Unlike scientific articles, the NIST investigation reports do not provide
enough information to be able to reproduce the models or any results derived from the
models.
Analyses from independent researchers regarding aircraft impact damage and collapse
scenarios have appeared during and after the official investigations. Earlier analyses were
severely limited by a lack of information and were overly simplified. Later analyses have
been more substantial, but as seen in Bazant et al. (2007)10, the mass and potential
energy are probably grossly overestimated.
Due to these limitations, many have questioned both the government’s specific account
of collapse initiation and the general theory of gravity-driven, progressive collapse. These
questions can only be answered by better modeling and a truly scientific approach. To be
valid, further analyses and models must be based on the correct mass and mass
distribution throughout the building.
The purpose of this paper is to establish a substantiated mass, mass distribution and
potential energy in World Trade Center Tower 1 (north tower) within a reasonable margin
of error. Here, the NIST “Federal Building and Fire Safety Investigation of the World
Trade Center Disaster” (called NCSTAR) documents provide a wealth of information
regarding the structural design, dimensions, building materials, contemporaneous
building codes and an approach to modeling.
3
3.1
Popular numbers
Many references can be found with different values for the mass of and the amount of
potential energy stored in the WTC twin towers. A number of references are shown in
Table 1 below. None of these references provide any data or calculation method on which
the mass and potential energy are based.
Note: Throughout this paper the term “ton” is used to designate the short or U.S. ton,
which is equal to 2000 lbs, and the term “metric ton” is used to designate 1000 kg.
Table 1: Different values for mass and potential energy
Source
Mass
Ashley 5
500,000 tons
Bazant et al. 10
576,000 tons *
Eagar and Musso 12
500,000 tons
4
Hamburger, et al. (FEMA)
Sunder et al. (NIST NCSTAR1) 8
> 250,000 tons
Tyson 2
500,000 tons
Potential Energy
> 4 E+11 J
* The Bazant et al. number is calculated here based on the following:
“Near the top, the specific mass (mass per unit height) µ = 1.02 × 106
kg/m. In view of proportionality to the cross section area of columns, µ =
1.05 × 106 kg/m at the impact level (81st floor) of South Tower.
Generally, we assume that µ(z) = k0ek2z + k1 (where k0, k1, k2 =
constants), with a smooth transition at the 81st floor to a linear variation
all the way down (precise data on µ(z) are unavailable). The condition
that ∫0 H µ(z)dz be equal to the total mass of tower (known to be almost
500,000 tons) gives µ = 1.46 × 106 kg/m at the base.” 10
Since µ(z) is unknown we can approximate the value for floors 82-110 using a linear
variation from the value at floor 81 to the value at floor 110 (29 floors) and the
proportion of the height for those floors. The height of WTC1 from the base to the roof is
437.69 m. The total number of floors is 116. µ(z)avg81-110 = 1.035 × 106 kg/m.
µ(z)avgB6-81 = 1.2475 × 106 kg/m.
Mass82-110 = µ(z)avg81-110 x (29/116) x h = 113.3 × 106 kg
MassB6-81 = µ(z)avgB6-81 x (87/116) x h = 409.5 × 106 kg
The total mass is then 522.8 × 106 kg or, converting to short tons, 576,000 tons. Bazant
et al. most likely assumed metric tons for the popular 500,000 ton number but that
doesn’t explain why we get 522.8 × 106 kg. The maximum error of using the linear
approximation instead of the exponential equation is less than 2 × 106 kg. If Bazant et
al. used the nominal height of the building (414.63 m from the concourse level to the
roof) the result would be 493.9 × 106 kg which corresponds better to the statement
“known to be almost 500,000 tons” assuming metric tons.
4
3.2
General overview of design and construction
A general description of the design and construction of World Trade Center Tower 1 is
beyond the scope of this paper. An excellent overview is given in NIST NCSTAR 1-1,
“Design, Construction, and Maintenance of Structural and Life Safety Systems.”
3.3
Original design
A number of original design documents are provided in NCSTAR1-1 and NCSTAR11A. NIST NCSTAR1-1A (p. 5)9 presents definitions from the original design as
follows:
1. “Floor inside of core”. That part of the floor bounded by the outside
faces of columns 501, 508, 1001 and 1008.
2. “Floor outside of core”. That part of the floor between the outside walls
and the “Floor inside of core”.
3. “Code live load”. The load specified in the New York Building Code for a
given occupancy.
4. “Live load for floor design”. The actual live load used for the design of
the parts of the floor which load may not be less than the “Code live
load”, and may be reduced for tributary areas as defined in “Live load
reduction”.
5. “Live load for column design”. The code live load, reduced as defined in
“Live load reduction” for columns.
6. “Construction dead load”. The weight of the bare structure (i.e. the slab
and beam) used in design of unshored composite beams.
7. “Construction live load”. The allowance for the weight of any equipment
and/or forms which is not permanent and does not form part of the total
load summation.
8. “Superimposed dead load”. The weight of ceilings, floor finish, walls or
partitions of known location, mechanical and electrical equipment and
similar items not included in the “Super imposed live load” or
“Construction dead load”.
9. “Dead load”. The sum of items 6 and 8 above.
10. “Superimposed live load”. The weight of the design live load, based on
occupancy, plus the weight of partitions if their location is subject to
change.
Essentially, the construction dead load (CDL), superimposed dead load (SDL) and
superimposed live load (SLL) together comprise all mass or weight in the building. Values
for CDL, SDL and SLL are also given in the design documents presented in NCSTAR1-1A
for some of the different types of floors within the building, inside and outside the core.
CDLs include steel used in floors such as beams, trusses, deck and concrete
reinforcement.
5
3.4
Amount of steel
NIST gives the total weight of structural steel in the two WTC towers as 200,000 tons.11
NIST describes steel contracts in NCSTAR1-3 (p.16), and the values are shown in Table 2
below.3 These contracts do not include trusses outside the core, steel deck, concrete
reinforcements or grillages.
Table 2: Weight of steel from supplier contracts
Structural component
Weight (short
tons)
external columns w/ spandrels
55 800
rolled core columns and beams
25 900
bifurcation columns
6 800
external box columns
13 600
core box below floor 9
13 000
core box above floor 9
31 000
slab supports below grade
12 000
total
158 100
3.5
Weight per tower
(short tons)
27 900
12 950
3 400
6 800
6 500
15 500
6 000
79 050
NIST reference models
In the NCSTAR1-2 series, NIST presents the methods used for developing the reference
structural models of the WTC towers. These models were used to assess the towers’
ability to withstand gravity and wind loads and to establish the reserve capacity in the
structures to withstand unanticipated events. According to NIST:
“The reference models included the following: Two global models of the
primary structural components and systems for each of the two towers
(and) two models, one of a typical truss-framed floor (tenant floor) and
one of a typical beam-framed floor (mechanical floor), within the impact
and fire regions. All reference models were linearly elastic and threedimensional, and were developed using the Computers and Structures,
Inc. SAP2000 software. SAP2000 is a commercial finite-element software
package that is customarily used for the analysis and design of
structures.” 7
The databases for the reference models were developed based on original structural
drawings. The databases were reviewed and checked against the original drawing books.
According to NIST:
“The original structural drawings of the WTC Towers were issued in two
main formats: (1) Large-size drawing sheets containing plan and elevation
information, and (2) Smaller book-sized drawings containing details and
tabulated information of cross-sectional dimensions and material
properties. The larger-sized drawings referred to the structural drawing
books in their notes, section and details. The structural databases,
developed in Microsoft Excel file format, were generated from these
drawing books and included modifications made after construction. The
databases were generated for use in the development of reference global
models of the towers.” 7
None of the original structural drawings were released by NIST. However, the larger
drawing sheets for WTC-1 (north tower) were leaked subsequently to the general public
and are generally available.17 The smaller drawing books still have not been made public.
6
3.6
NIST’s “Tower and Aircraft Impact Models”
NIST describes the “Tower and Aircraft Impact Models” in NIST NCSTAR 1-2. These
models were developed using the LS-DYNA 2003 software package.
“The WTC models for the impact analysis required considerably greater
sophistication and detail than was required for the reference models
described in Chapter 2. The reference models provided a basis for the
more detailed models required for the impact simulations. The impact
models of the towers, which utilized the structural databases described in
Chapter 2 (see also NIST NCSTAR 1-2A), included the following
refinements…” 7 (p. 93)
The loading of the structure for the analysis was determined by NIST as follows:
“The densities of the tower components (workstations and gypsum walls)
were scaled by the appropriate ratios to obtain the desired distribution of
live loads in the core and truss floor areas. The densities of all the
remaining tower structural components were scaled proportionately to
obtain the desired superimposed dead loads. These additional loads were
important for obtaining an accurate mass distribution in the towers and
inertial effects in the impact response. The in-service live load used was
assumed to be 25% of the design live load on the floors inside and outside
the core. The in-service live load was selected based on a survey of live
loads in office buildings (Culver 1976) and on engineering judgment.” 7 (p.
106)
NIST NCSTAR 1-2B (p. 53) gives an SDL (36.2 psf) which is in fact applied to the
structural components (columns).13 The SDL mass being applied to columns, is not a
problem when calculating the mass. However, the impact analysis must be significantly
affected by reducing the probability of debris coming into contact with core contents.
The effect is that impacting debris has a free shot at core structural members and is
more likely to pass all the way through the core. It is unclear if the partitions are
included in the SDL, SLL or both.
NIST NCSTAR 1-2B (p. 53) gives a summary of superimposed dead loads and live loads
and floor areas to which they are applied.13 The values are shown in table 3 below.
Table 3: Summary of superimposed dead loads and live loads
Area (sq ft)
Weighting (psf)
Core Dead Load (SDL)
8,694
36.2
Outer Dead Load (SDL)
31,257
11.5
Core Live Load
8,694
19.7
Outer Live Load
31,257
16.2
7
4
Method
The mass for the building is calculated on a floor by floor basis based on information in
the NIST reports and the architectural drawings. In some cases there are deviations from
NIST values and motivations for alternative values are described. In cases where there is
not enough information in the NIST reports, dimensions or materials are used from
similar areas of the building. As described in the introduction above, the design
documentation for WTC1 has the structural loads divided into construction dead loads,
superimposed dead loads, and superimposed live loads. These divisions are also used
here.
4.1
Floor Areas
According to NIST, the floor areas inside the core and outside the core are 8,694 sq ft
and 31,257 sq ft respectively (see Table 3). However, the architectural drawings give the
distance between the center of the external columns on one side to the center of the
external columns on the other side as 207’-8”.17 NIST gives the width of the external
column flanges as 13.5” and the spandrel thickness as 5/8”. Together these are roughly
14” contributing approximately 7” on each side to the 207’-8” dimension. Thus the
overall floor dimensions must be 206’-6” x 206’-6” with a gross floor area of 42,642 sq
ft. The outer dimensions of the core were 137’ x 85’ giving a gross core area of 11,745
sq ft. Thus the floor area outside the core is 30,897 sq ft. It may be that NIST subtracted
the areas taken up by core columns, elevator shafts and utility shafts in the core area,
which would account for the difference of roughly 25%. Generally in this analysis, the
floor areas used inside the core and outside the core are 11,745 sq ft and 30,897 sq ft
respectively.
For the purposes of establishing CDLs in the core, the floor areas inside the core were
adjusted to account for empty space due to elevator and utility shafts. The actual floor
areas were approximated by sampling a number of representative floors using the
architectural drawings.17 Two sizes of elevators predominated and the other shafts were
split into three groups: small, medium and large. The areas for the shafts in each group
were established by taking the dimensions of all shafts on floors 11-16 from the
architectural drawings (core plans), grouping them, and taking the average size for each
group.17 Elevators and shafts were then counted on the representative floors and
grouped by size. Elevators and shafts on average take up 41% of the core floor area. The
sampled floors, number of elevators and shafts, area with no floor, and the percentage of
empty space in the core are shown in Table 4. See Diagram 1 for examples of elevators
and shafts.
8
Table 4: Elevators and shafts on representative floors
count
count
count
count
count
elev. 1 elev. 2 shaft 1 shaft 2 shaft 3
89.5
203.8
10.5
27.3
48.1
floor
sq ft
sq ft
sq ft
sq ft
sq ft
6
27
23
12
16
0
14
27
23
9
8
10
26
15
23
10
10
10
33
15
23
10
10
10
41
3
23
10
10
10
50
26
14
11
7
6
66
14
12
12
8
7
77
3
14
11
5
6
83
24
2
8
5
5
94
19
2
11
5
5
105
7
2
8
4
5
average
area
w/ no
floor
sq ft
% core
7 231
62
7 462
64
6 456
55
6 456
55
5 385
46
5 508
47
4 153
35
3 401
29
2 974
25
2 559
22
1 429
12
4 819
41
Diagram 1: Example of architectural drawings - core plan floors 11-16. (Colored areas
with number designations are examples of the groups described above.)
9
4.2
Floor Types
A table of floors and diagrams of 15 different floor framing types are given in NIST
NCSTAR 1-2A, Appendix G (p192-196).14 The table shows which type of floor framing was
used for each particular floor. The diagrams show how the different types of framing (i.e.
truss or beam) were used in different floor types. The approximate percentages of truss
versus beam areas can easily be deduced from the diagrams. Unfortunately, there is no
indication of concrete types or thicknesses. For the purposes of this analysis, floors are
divided up into normal, mechanical, special and sublevel floors.
4.2.1
Normal Floors
All floors are considered normal unless they are mechanical floors, sublevels, or special
floors as described below. The floor numbers for normal floors are 10-40, 44-74 and 78106. These floors, which are predominantly offices and related areas, comprise eleven
floor types (type 1-11) that are predominantly truss framed. Some of these types have
sections of beam framed floor and two types have heavier angles or have reinforced
trusses. All of these floor types are treated as type 1 (100% truss framed) to simplify the
calculation of mass. The total error induced by this simplification is less than 1/1000 and
can be calculated as follows:
Err% = AAvg% x S% x (B-T)/B% = 0.073%
Where AAvg is the average proportion of beam area (1.45%), S = the floor
frame steel proportion of the total mass of the building (approx. 10%), T
is the truss design construction dead load (10 psf) 9 and B is the design
construction dead load (20 psf) 9 for beam framed floors. See table 5 for
calculation of AAvg.
Table 5: Floor types, count and beam framed area for calculation of average beam area.
Floor type Beam area/floor area count
1
0
74
2
0
3
3
0.0338
4
4
0.2772
1
5
0.2017
1
6
0
1
7
0.1689
1
8
0.1014
1
9
0.0338
4
*10
0.5
1
11
0
0
total
1.3168
91
avg %
0.0145
* Note: Floor 106 is type 10, which has reinforced trusses. The reinforced trusses are
assumed to be heavier than normal trusses and lighter than beam frames. Thus the floor
is given as being 50% beam framed to account for the extra weight for the purpose of
calculating the error due to simplification.
10
4.2.2
Mechanical floors
The mechanical floors are 7-9, 41-43, 75-77, and 108-110, which are all beam framed
floors. In each group of three floors, the upper and lower floors are type 12 and the
middle floor is type 13 (mechanical mezzanine). The mechanical mezzanines were 50%
open (no floor) outside the core so the floor area is 15,448.5 sq ft.
4.2.3
Sublevels
Sublevel floors were beam framed floors, designated B1-B6, and are type 14. As seen in
Table 2, 6000 tons of steel were used for slab support below grade. There is a minor
discrepancy between the NIST documentation and the architectural drawings. In the
architectural drawings, the floor below floor 1 is called the “Service Level” and the five
floors below are named B1-B5.
4.2.4
Special floors
Special floors include the Concourse level (floor 1), Plaza level or mezzanine (floor 2),
and the roof, which are beam framed floors. Floors 3-6 had no floors outside the core.
The Concourse level which was a high pedestrian traffic area is type 14 and probably had
stronger than normal floors. The Plaza level was type 15 and was partially open. Floor
107 was the restaurant “Windows on the World” and had beam-framed floors.
4.3
Gravity Loads
4.3.1
Foundation
The mass of the foundation provides no load on structural components other than itself
and contributes a negligible amount to potential energy. The mass of the foundation is
nonetheless approximated based on the film footage from the Port Authority of New York
and New Jersey.1 Dimensions are established by comparison to objects of known size, i.e.
humans. The total mass of the foundation is shown in Table 7.
The foundation for the core columns was comprised of steel reinforced concrete footers
and steel grillages built up out of I-beams. One steel grillage is made up of 17 I-beams,
each with approximate dimensions 0.75m x 0.2m x 2m and a plate thickness of around
0.03m. Each grillage also had a base plate for the core column with average approximate
dimensions 1m x 1m x 0.1m. It is assumed that there is one grillage per core column.
Using a density of 7.784 metric tons per cubic meter for the density of A36 steel, the
total mass for the grillages is approximately 484 metric tons. Each grillage was placed on
a concrete footer with approximate dimensions 2.5m x 2.5m x 2m. Using a density of 2.4
metric tons per cubic meter, the total mass for the concrete footers was approximately
1410 metric tons.
The foundation for the external columns was comprised of a continuous, steel reinforced,
concrete footer and base plates ranging from 7 to 9 sq ft (approx. 0.74 m2).6 The
thickness of the base plate is unknown but a thickness of 3 cm is assumed. Using a total
number of 80 exterior columns (transition to 238 columns at 7th floor), the total mass of
the base plates is approximately 14 metric tons. The concrete footer for the external
columns had a perimeter of 252 m. The other dimensions of the footer are unknown but
11
are approximated using 2 m for depth and 2 m for width. The total mass for the concrete
footer was approximately 2420 metric tons.
Table 6: Mass of the foundation
Component
Core steel grillage w/ base plate
Core concrete footer
External column steel base plates
External column concrete footer
Total mass foundation
4.3.2
Mass
(short tons)
513
1555
15
2670
4753
Mass
(metric tons)
466
1410
14
2420
4310
Amount of Core Column Steel
As described in the introduction, the steel contracts included 6,500 tons for core box
columns below the 9th floor, 15,500 tons for core box columns above the 9th floor and
12,950 short tons for rolled columns and beams. The amount of steel attributed to rolled
columns (wide flange shapes) is calculated in Appendix 2 as 3,268 short tons. Thus the
total core column steel is 25,268 short tons.
4.3.3
Variation of Core Column Steel
Core columns dimensions have been extracted from NIST’s SAP2000 model, which was
released based on a Freedom of Information Act (FOIA) request. These dimensions are
currently available on the internet.15 It can be seen in this data that the variation of core
columns steel is non-linear in the areas from floor B6 to floor 7 and from floor 107 to the
roof. There are also non-linear variations at the mechanical floors where the columns
were somewhat heavier, but these are ignored. The variation of core column steel mass
is shown in Table 7, which is based on calculations of core column steel per floor for
selected floors (see Table 19 in Appendix 3).
Table 7: Variation of Core Column Steel
Floor range
Variation
B6-001
Linear
002-007
Individual floor
008-053
Linear
054-106
Linear
107
Individual floor
108
Individual floor
109
Individual floor
110
Individual floor
111(roof)
Individual floor
Varies from (tons)
380.63
n.a.
427.14
181.57
n.a.
n.a.
n.a.
n.a.
n.a.
Varies to (tons)
427.14
427.14
181.57
30.91
35.81
41.42
35.81
35.81
31.20
When the core column steel mass is varied in this manner, the total core column steel
becomes 24,576 tons with 5,801 tons below floor 9. This amount of core column steel
below floor 9 should be 6,500 tons according to the steel contracts. This discrepancy may
be due to errors in the SAP2000 model, errors extracting data from the SAP2000 model
or maybe the contract included cross bracing not seen in the model data. Regardless, an
extra 699 tons is distributed evenly among the floors below floor 9 based on the
assumption that the steel contracts were correct at least in terms of the amount of steel.
The resulting total core column steel mass becomes 25,275 tons which correlates well
with the amount of core column steel calculated in the previous section (25,268 tons,
based on steel contracts and the calculation of rolled core columns in Appendix 2).
12
4.3.4
Amount of External Column Steel
As described in the introduction, the steel contracts included 6,800 tons for external box
columns, 3,400 tons for bifurcation columns and 27,900 tons for external columns
(prefabricated panels). The external box columns were used below floor 6. The
bifurcation columns were used between floors 6 and 9. The prefabricated panels included
spandrels. It is unclear if the other steel contract values for box and bifurcation columns
included spandrels but it is assumed that they did.
4.3.5
Variation of External Column Steel
There is no information given by NIST regarding the external box column dimensions so
the mass is distributed evenly between floor B6 and floor 5. The mass for the bifurcation
columns is distributed evenly over floors 6-8.
4.3.5.1
Above Floor 9
NIST NCSTAR1-3 describes the variation of spandrel thickness from 1.375 in. at floor 9 to
0.375 in. at floor 107. Also described is the external column flange thickness (above floor
9) varying from 3 in. to 0.25 in. at the top of the building. Since the exterior panels are
given in the steel contracts as a single value the mass must be divided between the
columns and the spandrels to give an accurate variation for both.
A rough distribution of the steel between the columns and spandrels can be done by
calculating the spandrel mass based on a linear variation between floors 9 and 111
(roof). However, the problem arises that there is not enough steel left to do a similar
linear variation for the external columns. This is most likely due to the fact that the
variation is not linear and actually has more weight lower in the building, similar to the
core columns. Thus a scale factor is used on the average column flange thickness and
spandrel thickness to arrive at the amount of steel as given in the steel contracts as
shown in Table 8.
Table 8: Distribution
flange
t
exterior col
min
0.250
max
3.000
avg (scaled)
1.467
spandrel
min
0.375
max
1.375
avg (scaled)
0.790
of mass between external columns and spandrels
web
volume cnt/ mass
w
h cnt
t
w
h cnt cu ft floor tons
13.5 144
13.5 144
13.5 144
2 0.25 13.500 144
2 0.25 13.500 144
2 0.25 11.065 144
120
120
120
1
1
1
58
58
58
2
2
2
1.1250
7.3125
3.7626
232 6 458
233 42 161
232 21 600
1.5104
5.5382
3.1824
80 2 990
80 10 963
80 6 300
total
scale factor
27 900
0.9030
Note: t = thickness, w = width and h = height (in inches), cnt = the number of plates
and the number of columns or spandrels, mass = volume x cnt x 101 floors x 490 lbs/cu
ft (converted to tons).
Thus, the steel mass allocated to the external columns and spandrels is 21,600 tons and
6,300 tons respectively. These masses are scaled linearly using proportions based on the
minimum and maximum values from NIST which results in a slightly higher proportion of
the mass higher in the building.
13
4.3.6
Gravity Loads for Normal Floors
In NIST NCSTAR1-2A, the baseline performance of the reference model is described
under several loading cases corresponding to the full design loads from the original
design, New York City Building Code (2001) and ASCE7-02 standard. It is not stated
explicitly but it appears that all loading cases used live load reduction in accordance with
the code.
4.3.6.1
CDLs inside the Core (normal floors)
Unit dead loads for concrete slabs inside the core are given in NIST NCSTAR1-1A (pp. 710). Both lightweight and normal concrete are specified as well as thicknesses ranging
from 4.35 in. to 5.5 in. There is no information which type of concrete or thickness was
used in any particular location. The design document on page 7 is for “unit dead load”
and there is no indication of floors to which they apply. This may indicate that this was
just a list of material unit dead loads. NIST NCSTAR1-2A (p.56) states that inside the
core the normal floors slabs were normal concrete and had a thickness of 4.5 in.
However, no source is given for this claim.
The design document on page 9 is for “unit design load” for floors 1-110 and indicates
that both lightweight and normal concrete were, in fact, used in the dead load design.
This document also gives an average slab thickness of 4.35 in. Unit design loads are
given for different floor finishes, but there is no specification of where these were used.
For the purposes of this analysis, normal concrete with a thickness of 4.35 in. is used
except on mechanical floors. As seen below, design SDLs and SLLs within the core are
similar to outside the core for normal floors, which have lightweight concrete floors with
a thickness of 4.35 in. Consequently, it would not be unrealistic to assume that
lightweight concrete was used for some or all floors in the core. Due to the fact that
normal concrete is 33% (18 psf) heavier and the difficulty in determining the locations of
various floor toppings, the extra weight is assumed to account for some variation of
concrete types and floor toppings, which range from 2-24 psf. The unit dead load for
normal concrete with thickness 4.35 in. is 54.38 psf.
Original design dead loads for steel floor components in the core are not found in the
NIST NCSTAR documentation. Nonetheless, reasonable values for steel CDLs can be
deduced from the beam framed floors outside the core.
CDLs for beam floor framing outside the core are given for mechanical floors 41 and 75
in NIST NCSTAR1-1A (p.12) as slab reinforcement = 3 psf, steel deck = 2 psf, and steel
beam = 20 psf. Since these beams include long spans of up to 60 ft., the beams are
most likely heavier than beams within the core where the maximum span is
approximately 20 ft, as seen in the architectural drawings.17 Thus, the core beam unit
dead load is assumed to be the average, of truss and beam framed floors outside the
core, which is 15 psf. In fact, NIST NCSTAR1-2A (p.70) gives a value of 6 to 7 psf used
in the reference model, but it is unclear if this was applied to the gross core area or just
the area with floor slabs. If these values were applied to the gross area it would be
roughly equivalent to applying 15 psf to the actual floor slab areas (avg. 59%). The
mechanical floors had much higher combined SDLs and SLLs than the core on normal
floors, so the slab reinforcement is assumed to be the same as truss framed floors, which
is 1.5 psf.
Unit CDLs for normal floors in the core including concrete slab, beams, steel decking and
reinforcement as well as the total unit CDL are shown in Table 9. The CDLs are only
applied to the portion of the core that actually has a floor.
14
Table 9: Normal Floors - Core component unit CDLs and total unit CDL
Component
Unit dead load psf
concrete slab
54.38
beams
15.00
steel decking
2.00
reinforcement
1.50
total
72.88
4.3.6.2
SDLs Inside the Core (normal floors)
NIST provides design documents which give unit dead loads inside the core for different
types of partitions, fireproofing, ceilings, and floor finishes, but no information is given as
to where they are applied on normal floors. As seen below, example SDLs are provided
for core areas on floor 96, but it is not clear if, or where, these apply to other floors. No
information is given regarding specific core contents such as pipes, cables, ducts, etc.
Nonetheless, NIST did calculate gravity loads for all floors inside the core based on
architectural drawings 17 and the original design criteria. Relevant information for normal
floors inside the core is as follows:
NIST NCSTAR1-1A
Partition loads are given in original design documents on p. 9 as “N.Y. code
uniform equivalent” 6 psf and 12 psf. SDLs for fireproofing outside the core
are given in NIST NCSTAR1-1A (p.12) for mechanical floors as 5 psf and 3
psf for the floors above. It is assumed that the mechanical floors required
extra fireproofing to avoid a fire spreading to the mechanical area, so a unit
dead load of 3 psf is assumed within the core. Unit SDLs for ceilings ranged
from 2-10 psf but there is no information which ceiling types were used in
specific areas. The ceiling unit SDL for the mechanical floors outside the
core is 3 psf, but the ceiling is most likely the one hanging from the floor
and hence the ceiling for an office area. The lighter types of ceiling are
assumed to be more prevalent, so a weighted average unit dead load of 3
psf is assumed for ceilings.
NIST NCSTAR1-2A
Section 4.2.2 (pp. 70-72) gives SDLs for partition groups from 6 to 44 psf.
This seems not to agree with the original design documents which give 6
and 12 psf as uniform code values. The actual values used in reference
model (SAP2000) on particular floors are not provided except for floor 96.
This section also describes floors B5, B3 to 9, 43 and 77 as mostly having
concrete encasement for fireproofing on beams, so fireproofing on normal
floors inside the core is assumed to be spray-applied fire resistant materials
(SFRM). Section 6.2.1 (p. 137) gives SDLs for five core areas on floor 96
ranging from 29-49 psf.
NIST NCSTAR1-2B
Chapter 3 describes development of the Tower Impact Model. Unit SDL for
impact floors is given on page 53 as 36.2 psf. This unit dead weight may be
applied to an area of only 8,694 sq ft, so it is possible that the total SDL for
the core is underestimated in that model.
The SDLs given in NIST NCSTAR1-2A for five core areas (29-49 psf) and the SDL given in
NIST NCSTAR1-2B (36.2 psf) seem to indicate an average unit SDL for normal floors
15
inside the core of around 40 psf. This value is assumed and is applied to the entire core
area on all normal floors. A reasonable break-down of the SDLs as well as the total unit
SDL are shown in Table 10.
Table 10: Normal Floors - Core component unit SDLs and total unit SDL
Component
Unit dead load psf
partitions
12.00
floor finish (avg.)
8.00
fireproofing
3.00
ceiling
3.00
other *
14.00
total
40.00
* Note: “Other” includes items such as pipes, electrical cables, ducts, mechanical
equipment, etc.
4.3.6.3
SLLs inside the core (normal floors)
Unit live loads within the core are given in NIST NCSTAR1-1A for different occupancy
types and usages ranging from 40-100 psf. Exceptions are floor 109 which had 150 psf
throughout and areas occupied by equipment which had none. For the impact analysis,
NIST NCSTAR1-2 (p.106) states:
“The in-service live load used was assumed to be 25% of the design load on
the floors inside and outside the core. The in-service live load was selected
based on a survey of live loads in office buildings (Culver 1976) and
engineering judgment.” 7
Another analysis based on a survey of live loads in Sydney, Australia (Choi 1989),
gives the mode for sustained live loads as 0.05 kPa (1 psf) for floor areas 2.5-5.0
m2 and 0.45 kPa (9.4 psf) for floor areas greater than 80 m2.16 A trend towards
higher load intensity for larger notional bays was identified. The mean for sustained
live loads was approximately 0.50 kPa (10.4 psf) for floor areas greater than 80
m2. This survey included offices, parking and plants rooms (mechanical). It is
unclear if partitions were included in the live loads.
NIST NCSTAR1-2B gives live loads, based on 25% of the design load, as 19.7 psf
inside the core and 16.2 psf out
side the core. This would imply an average
design load of 80 psf inside the core and 65 psf outside the core. NIST applies
these loads to the entire core area and the outer floors. It should be noted that the
live load should only be applied to areas with actual floors in the core (average
59%). On the other hand, NIST uses a floor area inside the core of 8,694 sq ft, but
it is unclear where this number comes from. There is no indication that live load
reduction was applied within the core.
For the purposes of this analysis, the in-service live load inside the core is assumed
to 19.7 psf for all normal floors, but this load is only applied to areas with actual
floor.
4.3.6.4
CDLs outside the Core (normal truss-framed floors)
NIST NCSTAR1-1A (p.11) provides design documents for truss framed floors
outside the core. A lightweight concrete slab with thickness 4.35 in. (36.5 psf) is
specified along with slab reinforcement (1.5 psf), steel deck (2.0 psf) and
structural steel (trusses, 10 psf). The total unit CDL is thus 50 psf.
16
4.3.6.5
SDLs outside the Core (normal truss-framed floors)
NIST NCSTAR1-1A (p.11) provides an original design document for truss framed
floors outside the core. Components specified are ceiling (2.0 psf), mechanical and
electrical (2.0 psf), floor finish (2.0 psf) and fireproofing (2.0 psf). SDLs for wall
finish and windows are not provided. NIST NCSTAR1-2A (p.136) indicates that SDL
allowances were 11.5-13.5 psf. If this includes wall finish and windows, the SDL for
those components would be on average 160 lbs per linear foot of external wall,
which seems reasonable. Thus the average unit SDL for normal truss framed floors
is assumed to be 12.5 psf.
4.3.6.6
SLLs outside the Core (normal truss-framed floors)
NIST NCSTAR1-1A (p.19) provides an original design document for the floor slab
which specifies 100 psf for live load. Column design is given on p. 20 which
specifies 50 psf live load (to be reduced according to code) and a 6-12 psf partition
allowance. NIST NCSTAR1-2B presents live loads, based on 25% of the design
load, as 16.2 psf outside the core which implies an average design load of 65 psf
outside the core. On page 136 there is a diagram of reduced live loads and how
they are applied to long span, two-way and short span truss areas. Here partition
allowances appear to be included in the reduced live loads and the average
reduced live load is approximately 65 psf. This corresponds well with Choi (1989) if
a 6 psf partition allowance is added to the survey’s mean sustained live loads (10.4
psf) in that study. The average unit live load for normal truss-framed floors is thus
assumed to be 16.2 psf including partition allowances.
4.3.7
Gravity Loads for Mechanical Floors
4.3.7.1
CDLs inside the Core (mechanical floors)
Unit dead loads for concrete slabs inside the core are given in NIST NCSTAR1-1A (pp. 710). Both lightweight and normal concrete are specified as well as thicknesses ranging
from 4.35 in. to 5.5 in. There is no information which type of concrete or thickness was
used in any particular location. The design document of page 7 is for “unit dead load” and
there is no indication of floors to which they apply. This may suggest that this was just a
list of material unit dead loads. NIST NCSTAR1-2A (p.57) states that inside the core the
mechanical floor slabs were normal concrete and had a thickness of 6 in. as well as a 2
in. topping slab. However, no source is given for this claim. The design document on
page 9 is for “unit design load” for floors 1-110, suggesting that both lightweight and
normal concrete were in fact used in the dead load design. This document also gives an
average slab thickness of 4.35 in. Unit design loads are given for different floor finishes,
but there is no indication where these were used. For the purposes of this analysis,
normal concrete with a thickness of 6 in. is used for mechanical floors.
Dead loads for steel floor components in the core are not found in the NIST NCSTAR
documentation. Nonetheless, reasonable values for steel CDLs can be deduced from the
beam framed floors outside the core.
CDLs for beam floor framing outside the core are given for mechanical floors 41 and 75
in NIST NCSTAR1-1A (p.12) as slab reinforcement = 3 psf, steel deck = 2 psf, and steel
beam = 20 psf. Since these beams include long spans of up to 60 ft., the beams are
most likely heavier than beams within the core where the maximum span is
approximately 20ft, as seen in the architectural drawings.17 Thus, the core beam unit
dead load is assumed to be the average of truss and beam framed floors outside the core
which is 15 psf. In fact, NIST NCSTAR1-2A (p.70) gives a value of 6 to 7 psf used in the
17
reference model, but it is unclear if this was applied to the gross core area or just the
area with floor slabs. If these values were applied to the gross area it would be roughly
equivalent to applying 15 psf to the actual floor slab areas (avg. 59%). Slab
reinforcement is assumed to be the same as beam framed floors outside the core, which
is 3 psf.
Unit CDLs for mechanical floors in the core including concrete slab, beams, steel decking
and reinforcement as well as the total unit CDL are shown in Table 11. The topping slab
is included in the SDL. The CDLs are only applied to the portion of the core that actually
has a floor.
Table 11: Mechanical Floors - Core component unit CDLs and total unit CDL
Component
Unit dead load psf
concrete slab
75.00
beams
15.00
steel decking
2.00
reinforcement
3.00
total
95.00
4.3.7.2
SDLs inside the Core (mechanical)
NIST provides design documents which give unit dead loads inside the core for different
types of partitions, fireproofing, ceilings and floor finishes, but there is no information
regarding where they are applied on mechanical floors. As seen below, example SDLs are
given for core areas on floor 96, but it is not clear if, or where, these apply to other
floors. No information is given regarding specific core contents such as pipes, cables,
ducts, etc. Nonetheless, NIST did calculate gravity loads for all floors inside the core
based on architectural drawings and the original design criteria. Relevant information for
mechanical floors inside the core is as follows:
NIST NCSTAR1-1A
Partition loads are given from original design documents on p. 9 as “N.Y.
code uniform equivalent” 6 psf and 12 psf. SDLs for fireproofing outside the
core are given in NIST NCSTAR1-1A (p.12) for mechanical floors as 5 psf
and 3 psf for the floors above. It is assumed that the mechanical floors
required extra fireproofing to avoid a fire spreading to the mechanical area,
so a unit dead load of 5 psf is assumed. Unit SDLs for ceilings ranged from
2-10 psf but there is no indication which ceiling types were used in
particular areas. The ceiling unit SDL for the mechanical floors outside the
core is 3 psf, but the ceiling is most likely the one hanging from the floor
and hence the ceiling for an office area.
NIST NCSTAR1-2A
Section 4.2.2 (pp. 70-72) gives SDLs for partition groups from 6 to 44 psf.
This does not agree with the original design documents which give 6 and 12
psf as uniform code values. The actual values used in reference model
(SAP2000) on particular floors are not given except for floor 96. This section
also describes floors B5, B3 to 9, 43 and 77 as mostly having concrete
encasement for fireproofing on beams with a unit dead load of 20 psf.
Section 6.3.1 (p. 141) gives SDLs for ten core areas on floor 75 ranging
from 25-141 psf. A topping slab is described with a thickness 2 in. and a
unit dead load of 20 psf.
18
On floor 75, it can be seen in the architectural drawings that the heavier areas take
up approximately 18% of the core area while elevator and service shafts take up
approximately 30%.17 Using 30 psf for shafts, 141 for heavy areas and 66 psf for
other areas, a weighted average gives 70 psf over the entire core. Floor 76 is
similar and is also assumed to have an average unit SDL of 70 psf. However, it can
be seen from the architectural drawings that floors 7-8, 41-42, and 108-109 are
more similar to normal floors inside the core so 40 psf is assumed for these
floors.17 Most floor areas inside the core above the mechanical floors (9, 43, 77)
had occupancies and usages similar to normal floors (see above SDL=40 psf), but
the concrete beam encasements add 20 psf giving 60 psf over the entire core for
these floors.
A reasonable break-down of the SDLs for mechanical floors inside the core as well as the
total unit SDL are shown in Table 12.
Table 12: Mechanical Floors - Core component average unit SDLs and average total unit
SDL
Component
Unit dead load psf
partitions
12.00
floor finish
20.00
fireproofing
5.00
ceiling
2.00
other *
31.00
total
70.00
* Note: “Other” includes items such as pipes, electrical cables, ducts, mechanical
equipment, etc.
4.3.7.3
SLLs inside the core (mechanical floors)
Unit live loads within the core are given in NIST NCSTAR1-1A for different occupancy
types and usages ranging from 40-100 psf. Exceptions are floor 109 which had 150 psf
throughout and areas on all floors occupied by equipment which had none. There is no
indication that live load reduction was applied within the core. In NIST NCSTAR1-2A, the
baseline performance is described under several loading cases corresponding to the
original design, New York City Building Code (2001) and ASCE7-02 standard. It is not
stated explicitly but it appears that all cases used live load reduction. For the impact
analysis, NIST NCSTAR1-2 states:
“The in-service live load used was assumed to be 25% of the design load on
the floors inside and outside the core. The in-service live load was selected
based on a survey of live loads in office buildings (Culver 1976) and
engineering judgment.”
NIST NCSTAR1-2B gives live loads inside the core, based on 25% of the design
load, as 19.7 psf which is applied to the entire core area. This would imply an
average design load of 80 psf inside the core. It should be noted that the live load
should only be applied to areas with actual floors in the core (average 59%). On
the other hand, NIST uses a floor area inside the core of 8,694 sq ft, but it is
unclear where this number comes from.
For the purposes of this analysis, the in-service live load inside the core is assumed
to be 19.7 psf for mechanical floors except floor 109, but this load is only applied
to areas with actual floor. The in-service live load inside the core is assumed to be
37.5 psf for floor 109.
19
4.3.7.4
CDLs outside the Core (mechanical beam-framed floors)
NIST NCSTAR1-1A (p.12) provides original design documents for beam framed
mechanical floors 41, 43, 75 and 77 outside the core. Floors 41 and 75 are lower
mechanical floors and had one specification while floors 43 and 77 were floors
above the mechanical areas which had another specification. The unit CDL given
for floors 41 and 75 is 94 psf. All lower mechanical floors (floors 7, 41, 75 and 108)
appear to be similar and are assumed to have the same specifications. All
mechanical mezzanines (floors 8, 42, 76 and 109) are also assumed to have a unit
CDL of 94 psf but with half the area. The unit CDL given for floors 43 and 77 is 125
psf. All floors above the mechanical areas (9, 43, 77 and 110) are assumed to have
the same specifications.
4.3.7.5
SDLs outside the Core (mechanical beam-framed floors)
NIST NCSTAR1-1A (p.12) gives a unit SDL for floors 41 and 75 as 116 psf
(including 75 psf of mechanical equipment). All lower mechanical floors (floors 7,
41, 75 and 108) appear to be similar and are assumed to have the same
specifications. The unit SDL given to floors 43 and 77 is 55 psf. All floors above the
mechanical areas (floors 9, 43, 77 and 110) are assumed to have the same
specifications. No unit SDL is provided for the mechanical mezzanines. The
mezzanines were most likely used for lighter equipment so the SDL is assumed to
be the same as lower mechanical floors minus 25 psf. Thus the mechanical
mezzanines (floors 8, 42, 76 and 109) are assumed to have a unit SDL of 91 psf.
4.3.7.6
SLLs outside the Core (mechanical beam-framed floors)
NIST NCSTAR1-1A (p.12) gives a design unit SLL of 75 psf for floors 41 and 75. All
lower mechanical floors (floors 7, 41, 75 and 108) appear to be similar and are
assumed to have the same specifications. The mechanical mezzanines (floors 8,
42, 76) are assumed to have the same unit SLL as mechanical floors. In accord
with preceding motivations, the average unit SLL is assumed to be 25% of the
design values or 19 psf. The design unit SLL is not given for floors 43 and 77. All
floors above the mechanical areas (floors 9, 43, 77 and 110) were essentially
tenant floors and assumed to have the same SLL as normal floors outside the core,
which is 16.2 psf. NIST NCSTAR1-2A (p. 73) gives the unit SLL for floor 109 as 150
psf so 37.5 psf (25%) is assumed for that floor.
4.3.8
Gravity Loads for Sublevels
There is little information in the NIST documentation regarding the sublevel floors. It is
assumed that these floors were similar to lower mechanical floors except that floors B1B3 were primarily tenant storage areas. As mentioned above, 6,000 tons of steel were
used for slab support below grade. It is unclear how this steel was applied, but floor 1
(Concourse level) did not have unusual load requirements. It is assumed therefore that
this steel was applied to floors B1-B5. It can be seen in the architectural drawings that
there are 24 columns supporting the floors outside the core. Nonetheless, for the sake of
simplification, the entire 6,000 tons is included in the floor CDL evenly distributed over
the gross floor area minus empty core space (41,467.5 sq ft.) both inside and outside the
core. This results in a unit CDL of 57.88 psf for structural steel. Given the comparatively
large amount of structural steel, it is assumed that the floor slabs are also somewhat
heavier than mechanical floors. The floor thickness is assumed to be 8 in. with normal
concrete which gives a unit CDL of 100 psf for the concrete slab. The steel deck and slab
20
reinforcement are assumed to be the same as mechanical floors or 5 psf combined. The
total unit CDL is then 162.88 psf.
For all sublevels, it is assumed that the CDLs, SDLs and SLLs are the same as lower
mechanical floors (see above) except for B1-B3 for which the mechanical equipment (75
psf) is removed from the SDL.
4.3.9
Gravity Loads for Special Floors
The NIST documentation provides little information regarding loads on special floors.




4.3.10
Floors 3-6 are assumed to have the same CDLs as lower mechanical floors inside
the core and the same SDLs and SLLs as normal floors inside the core. Floors 3-6
had no floors outside the core.
The Concourse level and Plaza level, which were high pedestrian traffic areas, are
assumed to have the same CDLs and SDLs as lower mechanical floors without the
mechanical equipment. Since the Plaza level was partially open (approx. 42%),
the total CDL and SDL for that floor is reduced by this amount. The SLLs for these
floors is assumed to 25% of the design load (100 psf), which is 25 psf throughout.
Floor 107 is assumed to have the same CDL as lower mechanical floors and the
same SDL as normal floors. This floor has a design live load of 100 psf so the SLL
is assumed to be 25%, or 25 psf.
The roof was a beam-framed, type 12 floor with a CDL equivalent to the lower
mechanical floors (94 psf). The SDLs for the roof are not described, but there
must have been some type of roof finish. 5 psf is assumed for the SDL (roof finish
only) plus 375 tons for the antenna. The design SLL for the roof was 40 psf and is
assumed to be 25% or 10 psf.
Hat Truss
According to NIST NCSTAR1-1:
“At the top of each tower (floor 107 to the roof), an assembly of hat trusses
interconnected the core columns and the exterior wall panels. Diagonals of
the hat truss were typically W12 or W14 wide flange members. In addition,
four diagonal braces (18 in. by 26 in. box beams spanning the 35ft gap, and
18 in. by 30 in. box beams spanning the 60ft gap) and four horizontal floor
beams connected the hat truss to each perimeter wall at the floor 108
spandrel. The hat truss was designed primarily to provide a base for
antennae atop both towers…” 6
Little information is available for establishing the mass of the hat truss. A rough estimate
of the mass of the hat truss is as follows:
NIST NCSTAR1-6D (p. 170) shows a diagram (figure 4-3) which shows the modeled
portion of the hat truss.25 The box and floor beams described above are seen in this
diagram plus, what appears to be, 12 major members in the core with lengths of
approximately 50-70 ft. Using column 902 at floor 108 (to which it appears the hat truss
is connected) as a representative W14 shape, the cross sectional area would be 37.0 sq
in.15 For the 12 major members the steel volume would be around 185 cu ft which is the
same as approximately 45 tons using 490 lbs/ft2 for the density of steel. Assuming a
similar plate thickness (0.8 in.) for the box beams the cross sections would be
approximately 80 in2. There were 8 long span (approx. 64 ft long) and 8 short span box
beams (approx. 36 ft long). Together they account for 108 tons. It is unclear if the floor
beams described above were normal beam-framed floor members of if they were added
21
especially. Assuming they were added, that would account for another approximately 100
tons. So a rough estimate of the mass of the hat truss members gives 250 tons.
In NCSTAR1-2A (p.73), NIST describes using an additional uniform SDL of 20 psf to the
gross area inside the core to account for hat truss steel which was not included in the
model and concrete beam encasement on all floors 107-roof. For the purposes of this
analysis, additional uniform SDL of 20 psf to the gross area inside the core on floors 107roof. The mass of the hat truss (250 tons) is divided equally over floors 107-roof and
applied as SDL to the core (50 tons/floor).
4.3.11
Aluminum cladding and elevators
There is no information in the NIST reports regarding loads attributed to aluminum
cladding and elevators. These are assumed to be included in the design SDLs.
22
5
5.1
Results
Summary of Results
The in-service mass of Tower 1 (North Tower) of the World Trade is found to be 288,100
metric tons (317,500 short tons). The potential energy above the 1st floor is found to be
480,600 MJ.
5.2
Detailed Results
The calculation of mass and potential energy was done in an Excel spreadsheet. The
spreadsheet is too large to fit in this document and is therefore linked as a separate
document (pdf, xls, html). Sources and motivations for values used are found in the
Method section above. An explanation of the columns in the spreadsheet is given in Table
13.
Table 13: Description of Spreadsheet Columns for Calculation
Column name
Description
Floor
Floor number from ground level. There are 110 floors plus the roof.
Floor + 6
This is the floor count from the bottom of the building upwards. Since there are six
sublevels not counted in the usual “110 floors”, there are actually 117 floors
including the roof. This is used for distributing column steel over the height of the
building.
Column steel
Includes external spandrels
Core column steel tons
Mass of steel for core columns above each floor in US tons.
Core column steel kg x
10^3
Mass of steel for core columns above each floor in metric tons.
Ext. column steel tons
Mass of steel for external columns above each floor in US tons.
Ext. column steel kg x 10^3 Mass of steel for external columns above each floor in metric tons.
Ext. spandrel steel tons
Mass of steel for spandrels at each floor in US tons.
Ext. spandrel steel kg x
10^3
Mass of steel for spandrels at each floor in metric tons.
Total column steel kg x
10^3
Combined mass for core columns, external columns and spandrels in metric tons.
Exceptions: The grillage steel is also included in this column.
Floors inside of core
Core floor area is 11,745 sq ft
Area with floor %
The portion of the core area with concrete floor in percent.
Average unit CDL psf
Average unit CDL per floor inside the core in pounds per sq ft. Exceptions: The
foundation concrete is also included in this column.
Core CDL kg x10^3
Total CDL per floor inside the core in metric tons. Calculated from the psf value and
the actual area with floor.
Steel component of CDL
psf
Portion of CDL per floor inside the core attributed to steel beams, deck and concrete
reinforcement in pounds per sq ft.
Steel component of CDL
kgx10^3
Total CDL per floor inside the core attributed to steel beams, deck and concrete
reinforcement, in metric tons.
Average unit SDL psf
Average unit SDL per floor inside the core in pounds per sq ft. The average SDL is
applied to the entire core. Exceptions: The antenna is included in the roof. The hat
truss is added to floors 107-roof as 50 metric tons per floor and 20 psf over the
entire core area on those floors.
23
Core SDL kgx10^3
Total CDL per floor inside the core in metric tons.
Average unit SLL psf
The average unit SLL per floor inside the core in pounds per sq ft.
Core SLL kgx10^3
Total SLL per floor inside the core in metric tons.
Floors outside of core
Area outside the core is 30,897 sq ft
Average unit CDL psf
Average unit CDL per floor outside the core in pounds per sq ft.
Outer CDL kgx10^3
Total CDL per floor outside the core in metric tons. Exceptions: Floors 3-6 have no
floor outside the core and thus no CDL. Floors 8, 42, 76 and 109 have only half
floors outside the core.
Steel component of CDL
psf
Portion of CDL per floor outside the core attributed to steel beams, deck and
concrete reinforcement in pounds per sq ft.
Steel component of CDL
kgx10^3
Total CDL per floor outside the core attributed to steel beams, deck and concrete
reinforcement, in metric tons. Exceptions: Floors 3-6 have no floor outside the core
and thus no CDL. Floors 8, 42, 76 and 109 have only half floors outside the core.
Average unit SDL psf
Average unit SDL per floor outside the core in pounds per sq ft.
Outer SDL kgx10^3
Total SDL per floor outside the core in metric tons. Exceptions: Floors 3-6 have no
floor outside the core and thus no SDL. Floors 8, 42, 76 and 109 have only half
floors outside the core.
Average unit SLL psf
The average unit SLL per floor outside the core in pounds per sq ft.
Outer SLL kgx10^3
SLL for the floor outside the core in metric tons. Exceptions: Floors 3-6 have no floor
outside the core and thus no SLL. Floors 8, 42, 76 and 109 have only half floors
outside the core.
Total mass kgx10^3
Total mass for the floor and in the summary row, for the building in metric tons.
PE(MJ)
Potential energy for the floor relative to the 1 floor in MJ. In the summary row this is
st
the total potential energy of the building relative to the 1 floor. Exceptions: The total
mass of the antenna (340 metric tons) is taken halfway up the antenna at 469m
st
above the 1 floor.
st
24
6
6.1
Discussion
Comparison with Other Buildings
In order to provide a “reality check” for the mass of World Trade Center Tower 1, it can
be compared to other buildings in terms of mass per unit area. It can be seen in Table 14
that the much older Empire State Building and the “popular” mass of the World Trade
Center Tower do not fit in with other buildings contemporaneous to The World Trade
Center. The Twin Towers and other skyscrapers from the same time period ushered in a
new era of highly efficient structures with new design techniques and building materials.
Nonetheless, it is important to bear in mind that the values presented in Table 14 are
from internet sources and that the values are based on definitions of “floor area” which
are not always clear and may differ from one another. Further study might include
validating the mass and floor area values for the other buildings.
Table 14: Comparison of mass per unit area with other buildings
Building
Floor area
m2
Completed
Empire State Building
1931
254 000
World Trade Center (popular)
1970
459 500
World Trade Center
1970
459 500
John Hancock Center
1969
Sears Tower
6.2
1973
21
Mass kg
330 000 000
21
500 000 000
260 128
423 624
18
1299
1088
288 100 000
20
Mass
per
unit
area
kg/m2
626
174 180 000
19
670
201 852 000
18
476
Comparison to Values Extracted from SAP2000 model
Self-weight and load values extracted from the SAP2000 model have been posted by a
blogger known only as “Shagster” on the James Randi Educational Foundation forum.
These values are shown in Table 15. These are only preliminary values and have not
been corroborated. Subsequent analyses could try to validate these values.
NIST modeled 3 different cases using SAP2000: “the original design case”, “the state of
the practice case” and the “refined NIST case”. However, it is unclear which case is
represented by the data released under the FOIA request. Two different live loads are
given as LLA and LLW. The total mass is given in Table 15, including these live loads
individually and together. The average loads for the building’s gross floor area are given
in psf. The load values calculated in this paper are given for comparison.
Table 15:
Loads
self-weight +
CDL
SDL
SLL
total
SAP2000 SAP2000 SAP2000
w/ LLA
w/ LLW LLA+LLW SAP2000 Calculated Calculated
106 kg
106 kg
106 kg
avg psf
106 kg
avg psf
191.8
44.6
50.1
286.5
191.8
44.6
59.9
296.3
191.8
44.6
110.0
346.4
25
19.9
49.0
189.9
62.1
36.2
288.1
27.7
16.1
6.2.1
Comparison to CDL from SAP2000 Model
The calculated CDL matches the SAP2000 model value very closely. Since the hat truss
(0.25 x 106 kg) is taken as SDL in the calculation but is considered to be CDL by NIST
the difference becomes less than 1%.
6.2.2
Comparison to SDL from SAP2000 Model
The SDLs from the SAP2000 model and the calculated values are definitely not in
agreement. One way of checking the NIST model is to asses the average value after
excluding the mechanical floors. In accord with the original design SDLs, the mechanical
floors account for 15.2 x 106 kg leaving 29.4 x 106 kg for the other 104 floors. The
average SDL for these floors becomes 14.6 psf which seems low considering that no
areas in the core are given by NIST as having less than 29 psf and the typical truss
framed floor is described as having an SDL of 14-16.
The calculated SDL may be somewhat over-estimated due to the fact that tenant space
in the core, which has a lower SDL, is not considered. A quick approximation of tenant
space on floors 50-105 indicates that the tenant space ranged from 17-50% of the core.
Using NIST’s SDL from outside the core, (14 psf, which included a 6 psf partition
allowance) the total SDL would be reduced by approximately 2.5 x 106 kg. Also, the hat
truss (0.25 x 10 6 kg) is taken as SDL in the calculation, but it is considered as CDL by
NIST.
It is interesting to note that the over-estimation described above, the hat truss and the
SDL from the mechanical floors, taken together amount to 17.75 x 106 kg, which, if
added to the total SDL from the model becomes 62.35 x 106 kg. Consequently, it may be
that NIST missed applying the SDLs from the mechanical floors to the model.
6.2.3
Comparison to Live Loads from SAP2000 Model
In NIST NCSTAR1-2A (p. 69), the live loads for the three cases are described as identical
for a typical truss floor being 50 psf. This section is contradictory as the original design
load is also given as 100 psf. This section also states that live load reduction was applied.
Elsewhere in NIST NCSTAR1-2A (p. 137), live load reduction is described for the three
loading cases where the original design case is based on 100 psf. The reduced live loads
for the original design case range from 55-82.5 psf. The reduced live loads for the other
two cases range from 25-47 psf to which a 6 psf partition allowance is added. Also given
in this section of NCSTAR1-2A, are the live loads for various core occupancies, ranging
from 40-100 psf. The large majority of these are greater than 50 psf.
If the SAP2000 data was from the original design case, the average live load would
necessarily be greater than 50 psf, which indicates that the data must be from one of the
other cases. If either the LLA value or the LLW value is taken individually, the average
live load is less than 27 psf, which doesn’t correspond with any of the loading cases.
When comparing the SAP model live load to the average live load calculated in this
paper, it is important to remember that it is a comparison between live load permitted by
code and in-service live loads which are usually equal to or less than 25% of code or
design (as described in more detail above in the section “SLLs outside the Core (normal
truss-framed floors”). Thus the calculated value of 16.1 psf is actually slightly higher than
what would normally be expected.
26
6.3
Comparison to Total Column Loads in NIST Models
NIST NCSTAR1-6D (p. 176) presents total column loads for WTC1 and WTC2 models.25
The NIST loads are shown along with calculated loads for a number of floors in Table 16.
The percent difference is calculated relative to the NIST loads. It can be seen that the
floor mass trend is toward higher mass lower in the building for both the calculated and
NIST loads, as expected. Nonetheless, the floor mass variation is greater in the
calculated loads. In fact if the difference trend is extrapolated to the lowest floor, the
calculated total load would be 30% higher than the NIST total load at the base.
Table 16:
Floor
98-99
95-96
93-94
80-81
78-79
* NIST
Calc Mass
NIST Mass
1000 kg
1000 kg
30,972
33,177
36,521
37,775
40,252
40,850
64,971
*61,563
68,826
*64,749
mass from WTC2 model
Difference
-6.64%
-3.32%
-1.46%
5.54%
6.30%
In the calculated loads, the primary contribution to increasing mass lower in the building
is made by structural steel (columns and spandrels). Since this variation is based on the
SAP2000 data and other data from NIST, it is very difficult to explain this discrepancy.
6.4
6.4.1
Comparison to Amount of Debris Removed from Ground Zero
The Amount of Debris
Martin Bellew, Director of the Bureau of Waste Disposal, New York Department of
Sanitation states in an article on the AWPA website:
“200,000 tons of steel were recycled directly from Ground Zero to various
metal recyclers. The Fresh Kills Landfill received approximately 1.4 million
tons of WTC debris of which 200,000 tons of steel were recycled by a
recycling vendor (Hugo Neu Schnitzer).” 22
Phillips & Jordan, Inc. reported:
“The last debris was processed on July 26, 2002, day 321 of the project. At
the close of the Staten Island Landfill mission: 1,462,000 tons of debris had
been received and processed, 35,000 tons of steel had been removed
(165,000 tons were removed directly at Ground Zero).” 23
Thus the total amount of debris is 1,662,000 tons.
6.4.2
Calculation of Debris Amount
The calculated debris mass is 1.6 million tons. (See Appendix 1, Calculation of Debris
Amount.)
6.4.3
Comparison of Calculated Mass to Recovered Mass
The calculated debris mass (1.6 million tons) seems to correspond well with the reported
debris mass (1.66 million tons). Table 17 also includes a column for scaled mass
assuming the mass of the two towers to be the commonly stated 500,000 tons. The
other WTC Complex building masses are scaled in accord with the same proportions while
the rest of the debris is not scaled. The proportional scaling is based on the assumption
27
that if the WTC Towers were more massive, the rest of the buildings would also be more
massive. The resulting scaled debris mass of 2.44 million tons is roughly 50% more than
the reported amounts.
6.4.4
Conclusions
The calculated mass of 288,100 metric tons (317,500 short tons) is found to correspond
with two other comparable structures (in terms of mass per unit floor area), data from
NIST’s SAP2000 model, and the reported amount of recovered debris. The calculated
mass refutes the popular notion that the building weighed 500,000 tons. Further study
may be warranted to examine other contemporaneous structures, validate the SAP2000
model values, and establish a more reliable estimation of the distribution between
sources of removed debris.
28
7
References
1. Port Authority of New York and New Jersey, “Building the World Trade Center.” (1983)
http://www.pbs.org/wgbh/amex/newyork/sfeature/sf_building.html
2. Tyson, P., “Towers of Innovation.” PBS/NOVA
http://www.pbs.org/wgbh/nova/wtc/innovation.html
3. Gayle, F.W., et al., “NIST NCSTAR 1-3 Mechanical and Metallurgical Analysis of
Structural Steel.” NIST Federal Building and Fire Safety Investigation of the World
Trade Center Disaster http://wtc.nist.gov/reports_october05.htm
4. Hamburger, R., et al., (May 2002) “World Trade Center Building Performance Study,
Chapter 2: WTC1 and WTC2.” FEMA 403
http:/www.fema.gov/rebuild/mat/wtcstudy.shtm
5. Ashley, S., (October 09, 2001) “When the Twin Towers Fell.” Scientific American
6. Lew, H.S., Bukowski, R.W., Carino, N.J., “NIST NCSTAR 1-1 Design, Construction, and
Maintenance of Structural and Life Safety Systems.” NIST Federal Building and Fire
Safety Investigation of the World Trade Center Disaster
http://wtc.nist.gov/reports_october05.htm
7. Sadek, F., “NIST NCSTAR 1-2 Baseline Structural Performance and Aircraft Impact
Damage Analysis of the World Trade Center Towers.”, NIST Federal Building and
Fire Safety Investigation of the World Trade Center Disaster
http://wtc.nist.gov/reports_october05.htm
8. Sunder, S.S., et al., “NIST NCSTAR 1 Final Report on the Collapse of the World Trade
Center Towers.” NIST Federal Building and Fire Safety Investigation of the World
Trade Center Disaster http://wtc.nist.gov/reports_october05.htm
9. Fanella, D.A., Derecho, A.T., Ghosh, S.K., “NIST NCSTAR 1-1A Design and
Construction of Structural Systems.” NIST Federal Building and Fire Safety
Investigation of the World Trade Center Disaster
http://wtc.nist.gov/reports_october05.htm
10. Bazant, Z.P., Le, J.L., Greening, F.R., Benson, D.B., “Collapse of World Trade Center
Towers: What Did and Did Not Cause It?”, Structural Engineering Report No. 0705/C605c http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/00 WTC
Collapse - What did & Did Not Cause It - Revised 6-22-07.pdf
11. Banovic, S.W., “NIST NCSTAR 1-3B Steel Inventory and Identification” NIST Federal
Building and Fire Safety Investigation of the World Trade Center Disaster
http://wtc.nist.gov/reports_october05.htm
12. Eagar, T.W. and Musso, C., (2001) “Why Did the World Trade Center Collapse?
Science, Engineering, and Speculation”, JOM (The Journal of the Minerals, Metals
and Materials Society). 53(12), pp.8-11
http://www.tms.org/pubs/journals/JOM/0112/Eagar/Eagar-0112.html
13. Krikpatrick, S.W., “NIST NCSTAR 1-2B Analysis of Aircraft Impacts into the World
Trade Center Towers” NIST Federal Building and Fire Safety Investigation of the
World Trade Center Disaster http://wtc.nist.gov/reports_october05.htm
29
14. Faschan, W.J., Garlock, R.B., “NIST NCSTAR 1-2A Reference Structural Models and
Baseline Performance Analysis of the World Trade Center Towers” NIST Federal
Building and Fire Safety Investigation of the World Trade Center Disaster
http://wtc.nist.gov/reports_october05.htm
15. Water, L., “WTC Modelling and Simulation”, (on-line only)
http://wtcmodel.wikidot.com/nist-core-column-data
16. Choi, E.C.C., (December 1989), “Live Load Model for Office Buildings”, The Structural
Engineer, Volume 67, No.24/19, pp.421-437
17. “North Tower Blueprints” (Architectural Drawings), The World Trade Center: The Port
Of New York Authority, Minoru Yamasaki & Associates: Minoru Yamasaki, Architect,
Worthington, Skilling, Helle & Jackson: Structural Engineers, Joseph R. Loring &
Associates: Electrical Engineers, Emery Roth & Sons: Richard Roth, Architect, Jaros,
Baum & Bolles: Mechanical Engineers, The Port Of New York Authority, Paving,
Utilities, Foundations, http://911research.wtc7.net/wtc/evidence/plans/index.html
18. Sears Tower web site http://www.thesearstower.com/pdf/SearsTowerInfo.pdf
19. Wonders of the World Data Bank, Mass of John Hancock Center,
http://www.pbs.org/wgbh/buildingbig/wonder/structure/john_hancock.html
20. “John Hancock Center”, Wikipedia,
http://en.wikipedia.org/wiki/John_Hancock_Center
21. Empire State Building, Wikipedia, http://en.wikipedia.org/wiki/Empire_State_Building
22. Bellew, M. J., (March 2004), “Clearing the way for recovery at Ground Zero: The 911 role of the NYC Department of Sanitation”, American Public Works Association
web site
http://www.apwa.net/Publications/Reporter/ReporterOnline/index.asp?DISPLAY=IS
SUE&ISSUE_DATE=032004&ARTICLE_NUMBER=770
23. Phillips & Jordan, Inc., “Anatomy: World Trade Center/Staten Island Landfill Recovery
Operation”, Phillips & Jordan, Inc., Disaster Recovery Group web site
http://disaster.pandj.com/World%20Trade%20Center%20Forensic%20Recovery.pd
f
24. McAllisster T., et al., (May 2002) “World Trade Center Building Performance Study,
Chapter 7: Periferal Buildings” FEMA 403
http:/www.fema.gov/rebuild/mat/wtcstudy.shtm
25. Zarghamee, M.S., et al., “NIST NCSTAR 1-6D Global Structural Analysis of the
Response of the World Trade Center Towers to Impact Damage and Fire” NIST
Federal Building and Fire Safety Investigation of the World Trade Center Disaster
http://wtc.nist.gov/reports_october05.htm
30
8
8.1
Appendices
Appendix 1: Calculation of Debris Amount
While it is difficult to know exactly what was removed from ground zero, there are
numerous articles describing damage to the WTC complex and the surrounding areas.
There are also numerous photographs available on the internet of the damage as well as
the progress of the cleanup at various stages. The calculation shown in Table 17 is a very
rough estimate based on a wide range of sources. Sources are not cited as they are too
numerous for the scope of this study. Photos are not included because of usage rights
issues. Further study could include a detailed analysis of the debris as well as complete
presentation of motivations for assumptions as well as detailed sourcing.
31
Table 17: Calculation of Debris Amount
desc
WTC1
WTC2
WTC3 Marriott est.
25,000 sq ft x 22
stories
area sq ft stories
3 800 000
116
3 800 000
116
CDL +
SDL
psf
total
CDL +
SDL
kgx10^3
SLL psf
total SLL
kgx10^3
mass total
mass
kgx10^3
total tons
288 100
317 606
288 100
317 606
scaled
mass
500 001
500 001
540 000
22
140.00
34 292
16.20
3 968.09
38 260
42 179
66 401
WTC4
950 000
9
140.00
60 329
16.20
6 980.90
67 310
74 203
116 817
WTC5
1 080 000
9
140.00
68 584
16.20
7 936.19
76 521
84 357
132 802
WTC6
537 693
7
140.00
34 146
16.20
3 951.14
38 097
41 998
66 117
WTC7
1 868 000
47
112.00
94 900
16.20 13 726.66
108 627
119 752
188 523
Plaza btw 4+5
Concourse btw 4+5
(part not included in
4+5)
Basement 2 level WTC4, WTC5 and
under concourse
100 000
220.00
9 979
16.20
734.83
10 714
11 811
18 594
100 000
220.00
9 979
16.20
734.83
10 714
11 811
18 594
250 000
220.00
24 948
24 948
27 503
43 298
Bathtub ground level
398 792
220.00
39 796
0.00
0.00
39 796
43 872
69 067
Bathtub Concourse
398 792
220.00
39 796
25.00
4 522.30
44 319
48 857
76 915
Bathtub sublevel B1
398 792
225.00
40 701
50.00
9 044.60
49 745
54 840
86 334
Bathtub sublevel B2
398 792
225.00
40 701
50.00
9 044.60
49 745
54 840
86 334
Bathtub sublevel B3
398 792
300.00
54 268
50.00
9 044.60
63 312
69 796
109 879
Bathtub sublevel B4
398 792
300.00
54 268
50.00
9 044.60
63 312
69 796
109 879
Bathtub sublevel B5
398 792
300.00
54 268
50.00
9 044.60
63 312
69 796
109 879
210.00
4 763
15.00
340.20
5 103
5 626
8 856
Con Edison substation
50 000
total area
15 817 237
2
sq ft/cu ft
Cortland St Station 1/9
Cortland St Station N/R
psf/pcf
lbs
5 000.00
245.00
1 225 000
613
613
600.00
245.00
147 000
74
74
Subway 1/9 2500 ft double track

track

concrete
26.66
lb/ft
266 600
133
133
210 000
31 500 000
15 750
15 750
4 000.00
150.00
per
vehicle
5 600 000
2 800
2 800
debris from Winter Garden
45 000.00
200.00
9 000 000
4 500
4 500
debris from WFC3 American Express
30 000.00
150.00
4 500 000
2 250
2 250
1 800
1 800
10 000.00
160.00
1 600 000
800
800
8 000.00
160.00
1 280 000
640
640
1400 vehicles
debris from One WFC
debris from Bankers Trust Building
debris from 90 West St.
debris from Verizon Building
debris from 130 Cedar St.
debris from 30 West Broadway
earth excavated in front of WFC buildings
180 000
90.00
16 200 000
8 100
8 100
Vesey Street collapsed (20x50 ft.)
1 000.00
245.00
245 000
123
123
a portion of the slurry wall was destroyed and removed on the south
east side of the bathtub
12 000.00
150.00
1 800 000
900
900
Collapsed area in front of Bankers Trust
20 000.00
200.00
4 000 000
2 000
2 000
3 600.00
150.00
540 000
North bridge from Winter garden to WTC6
water
Total
32
270
270
88 418
1 595 420
88 418
2 437 462
8.1.1
Comments on Calculation of Debris Mass
The mass of destroyed buildings in Table 17 is calculated from assumed unit loads based
on the loads from WTC1. The average unit load from WTC1 was 128 psf. WTC 7 which
had a similar construction uses the same unit load. The other WTC complex buildings
were somewhat heavier due to a more conventional post and beam construction and are
assumed to have a unit load of 156 psf. WTC1 and WTC2 include sublevels, while the
other buildings do not. It can be seen in the architectural drawings that the area of the
sublevels within the bathtub, excluding WTC1 and WTC2 was close to 400,000 square
feet. The sublevels within the bathtub are assumed to be much more heavily
constructed, especially in the lowest levels due to very heavy mechanical areas such as
electrical substations and the cooling plant. Also much of the sublevels were used for
parking. The Con Edison substation is assumed to similar to the sublevels.
The calculated total floor area is roughly 16 million sq ft. FEMA gives the total office area
for the World Trade Center Complex as 12 million sq ft.24 There were no offices in the
sublevels which accounts for 2.1 million sq ft. This leaves 1.9 million sq ft which is 14%
of the remaining area. It is not unreasonable to assume that the rest of the areas had
14% of the space allocated for other uses such as service, utility, mechanical and transit.
Thus 16 million sq ft seems to be a reasonable number.
Notes on other debris:














The Cortland Street station for the 1/9 subway was completely destroyed.
The Cortland Street station for the N/R subway was damaged where external
columns from WTC1 penetrated Vesey St.
2500 ft of subway tunnel for the 1/9 were removed and replaced due to damage.
This line ran along the outside of the eastern wall of the bathtub.
1400 destroyed vehicles were removed to the Staten Island Landfill.
The Wintergarden, part of the World Financial Center (WFC) Complex was
severely damaged and mostly removed.
Eight floors with roughly 10 bays were removed from the southeast corner of the
American express building (WFC3).
The Verizon building had extensive facade damage and large portions of the
facade the east and south side were replaced.
130 Cedar St. had extensive damage to the roof where external panels from
WTC2 penetrated the structure.
30 West Broadway had extensive damage from the collapsing WTC7 building and
roughly 25 bays were completely destroyed.
Vesey Street collapsed where the debris from WTC7 landed.
In photographs taken during cleanup, it appears that at least 3 ft of earth were
excavated from in front of the WFC complex on the eastern side.
A portion of the slurry wall was destroyed by the collapse of WTC2. The
dimensions are approximately 3 ft x 100 ft x 20 ft.
The entire area in front of the Bankers Trust building collapsed.
The North Bridge from the Wintergarden to WTC6 was completely destroyed.
One easily overlooked factor is the amount of water that inundated nearly all debris
areas. Broken water mains and fire-fighting must have made the larger portion of
cementitious debris and earth heavier during removal. The value in Table 17 is based on
the total amount of concrete having the additional weight based on the density of wet
sand with stone aggregate.
Ignored factors:

A small portion of the sublevels at the northern end of the bathtub remained
intact.
33








8.2
Facade damage to all buildings except the Verizon building were ignored.
Large portions of the PATH train track were removed.
Absorption of water by debris other than cementitous materials, such as
pulverized gypsum wall board, fabric and wood based materials.
The amount of earth removed outside the bathtub.
The amount of material that was burned off in the fires.
Temporary structure materials for shoring and bridging.
Subway cars.
Debris from One WFC, the Bankers Trust building, and the building at 90 West St.
Appendix 2: Calculation of Rolled Core Column Mass
The transition from box shapes to wide flange shapes was identified based on the shape
images from the WTC Modeling and Simulation site for the transition floors.15 Rolled core
column dimensions (wide flange shapes) were taken from that site. The cross-sectional
area is assumed to vary linearly between the transition floor and floor 106. The mass for
all rolled core columns is 3,268 short tons.
In Table 18, the cross-sectional area for each column is calculated at the transition floor,
based on the dimensions given. Volume is calculated assuming a height of 12 ft. The
mass of the column on the transition floor is calculated using the density of steel (490
lbs/ft3). The mass of the columns at floor 106 is taken from Appendix 3. The total for the
column from the transition floor to floor 106 is calculated using the average between the
transition floor and the 106th floor and the number of floors. Floors 107, 108, 110 and
111 (roof) are calculated individually (see Appendix 3). Floor 109 had the same
dimensions as floor 110.
Table 18: Calculation of Mass from Core Column Wide Flange Data
t-floor
col
transition width depth
width depth
area volume short
nr
floor
in
in
cnt
in
in
cnt sq ft
cu ft
tons
501
83 12.58
3.07
1
17.9 4.91
2 1.4889 17.8666 4.3773
502
83 12.58
2.02
1
16.8 3.21
2 0.9255 11.1056 2.7209
503
83 12.58
2.02
1
16.8 3.21
2 0.9255 11.1056 2.7209
504
86 12.624 1.655
1 16.475 2.658
2 0.7533 9.0395 2.2147
505
66 12.624 1.545
1 16.365 2.468
2 0.6964 8.3568 2.0474
506
83
12.6 2.19
1
17
3.5
2 1.0180 12.2162 2.9930
507
83 12.624 1.875
1 16.695 3.033
2 0.8677 10.4118 2.5509
508
83 12.58
3.07
1
17.9 4.91
2 1.4889 17.8666 4.3773
601
86 10.908
1.08
1 12.67 1.736
2 0.3873 4.6476 1.1387
602
80 12.624 1.205
1 16.025 1.936
2 0.5365 6.4384 1.5774
603
80 12.624 1.205
1 16.025 1.936
2 0.5365 6.4384 1.5774
604
80 10.908
1.08
1 12.67 1.736
2 0.3873 4.6476 1.1387
605
86 10.908
1.08
1 12.67 1.736
2 0.3873 4.6476 1.1387
606
80 12.624
1.31
1 16.13 2.093
2 0.5837 7.0048 1.7162
607
80 12.624 1.125
1 15.945 1.813
2 0.5001 6.0015 1.4704
608
86 10.908
1.08
1 12.67 1.736
2 0.3873 4.6476 1.1387
701
95 10.908 0.905
1 12.515 1.486
2 0.3268 3.9222 0.9609
702
36 12.58
3.07
1
17.9 4.91
2 1.4889 17.8666 4.3773
703
75 12.624 1.545
1 16.365 2.468
2 0.6964 8.3568 2.0474
704
0
12.6 2.19
1
17
3.5
2 1.0180 12.2162 2.9930
705
7 12.624
1.31
1 16.13 2.093
2 0.5837 7.0048 1.7162
34
fl. 106
short
tons
1.2610
0.9425
0.8938
0.7080
0.8151
0.8938
0.8151
1.2610
0.3838
0.4304
0.4982
0.3120
0.3838
0.4982
0.4982
0.3838
0.5876
0.5641
0.2813
0.2512
0.2512
t-106
short
tons
76.12
49.46
48.80
35.07
61.54
50.53
43.76
73.30
17.51
29.11
30.10
21.03
17.51
32.11
28.54
17.51
10.84
180.36
39.59
176.81
100.34
706
707
708
801
802
803
804
805
806
807
808
901
902
903
904
905
906
907
908
1001
1002
1003
1004
1005
1006
1007
1008
8.3
45
7
89
95
33
95
9
36
27
89
12.624
12.624
10.908
10.908
12.58
10.908
12.58
12.624
12.58
12.624
1.875
1.205
1.08
0.905
3.07
0.755
2.02
1.875
3.07
0.98
1
1
1
1
1
1
1
1
1
1
16.695
16.025
12.67
12.515
17.9
12.365
16.8
16.695
17.9
15.8
86
48
80
77
86
48
48
48
80
77
77
86
86
77
77
80
10.908
12.6
12.624
10.908
10.908
12.58
12.56
12.624
12.58
12.56
12.56
12.624
12.624
12.58
12.6
12.58
1.08
2.19
1.415
1.08
0.905
2.02
2.38
1.875
3.07
2.83
2.83
1.545
1.415
2.6
2.19
3.07
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
12.67
17
16.235
12.67
12.515
16.8
17.2
16.695
17.9
17.7
17.7
16.365
16.235
17.4
17
17.9
3.033
1.936
1.736
1.486
4.91
1.236
3.21
3.033
4.91
1.563
2
2
2
2
2
2
2
2
2
2
0.8677 10.4118 2.5509
0.4013
94.47
0.5365 6.4384 1.5774
0.5409
108.04
0.3873 4.6476 1.1387
0.7922
19.31
0.3268 3.9222 0.9609
0.5898
10.86
1.4889 17.8666 4.3773
0.5641
187.77
0.2695 3.2335 0.7922
0.3838
8.23
0.9255 11.1056 2.7209
0.2315
147.62
0.8677 10.4118 2.5509
0.4380
109.10
1.4889 17.8666 4.3773
0.5409
201.65
0.4289 5.1469 1.2610
0.5641
18.25
0.0000 0.0000 0.0000
0.0000
0.00
1.736
2 0.3873 4.6476 1.1387
0.4256
17.99
3.5
2 1.0180 12.2162 2.9930
0.4982
106.48
2.283
2 0.6388 7.6660 1.8782
0.7080
37.50
1.736
2 0.3873 4.6476 1.1387
0.3675
24.10
1.486
2 0.3268 3.9222 0.9609
0.3120
14.64
3.21
2 0.9255 11.1056 2.7209
0.4982
98.18
3.62
2 1.0724 12.8684 3.1528
0.5641
113.36
3.033
2 0.8677 10.4118 2.5509
0.4256
90.78
4.91
2 1.4889 17.8666 4.3773
1.6595
87.53
4.52
2 1.3580 16.2961 3.9925
1.3978
86.25
4.52
2 1.3580 16.2961 3.9925
1.1519
82.31
2.468
2 0.6964 8.3568 2.0474
0.8151
32.92
2.283
2 0.6388 7.6660 1.8782
0.7559
30.29
4.16
2 1.2325 14.7897 3.6235
0.8151
71.02
3.5
2 1.0180 12.2162 2.9930
0.8938
62.19
4.91
2 1.4889 17.8666 4.3773
1.6595
87.53
Subtotal: transition floor - 106 3,088.28
floor 107
35.81
floor 108
41.42
floor 109
35.81
floor 110
35.81
roof
(111)
31.20
Total core columns (wide flange shapes) 3,268.31
Appendix 3: Core Column Data for Selected Floors
The data in Table 19 was collected from the WTC Modeling and Simulation site.15
For each column, the cross sectional area is given in sq ft and the volume for a 12-foot
high floor is given in cu ft. The mass is given in short tons based on the density of steel
(490 lbs/ft3).
35
Table 19: Core column data for selected floors
col
w
501
52
502
52
503
52
504
52
505
52
506
52
507
52
508
52
601
43
602
36
603
36
604
36
605
36
606
36
607
36
608
43
701
37
702
30
703
34
704 12.6
705
28
706
30
707
30
708
37
801
34
802
30
803
34
804
28
805
34
806
30
807
34
808
901
43
902
36
903
36
904
36
905
22
906
36
907
36
908
43
1001
52
1002
52
1003
52
1004
52
1005
52
1006
52
1007
52
1008
52
5
4.75
4.375
2.9375
3.375
5
4.625
5
3.625
3.375
3.125
2.375
2.5625
3.125
3.125
3.125
4.25
3.5
2.5
2.19
1.25
3
3.375
4.125
4.5
3.375
2.6875
1.75
2.375
3.25
4.25
cnt
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
2
2
2
2
2
2
2
1
2
2
2
12
12.5
13.25
16.125
11.25
12
12.75
12
6.75
9.25
9.75
9.25
8.875
9.75
9.75
7.75
6.5
19
11
17
14.5
11
19.25
6.75
6
19.25
9.625
13.5
12.25
19.5
6.5
floor B6-B3
cnt w
5
2 39
4.75
2
4.375
2
3
2
3.375
2
5
2
4.625
2
5
2 39
3.625
2
3.375
2
3.125
2
2.375
2
2.5625
2
3.125
2
3.125
2
3.125
2
4.25
2
3.5
2
2.5625
2
3.5
2
1.25
2
3.125
2
3.5
2
4.25
2
4.5
2
3.5
2
2.6875
2
1.8125
2
2.375
2
3.25
2
4.25
2
2.625
3.125
3
2
3.625
2.8125
3.25
2.625
5
5
5
3.25
3
4.75
4.875
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
8.75
9.75
10
10
6.75
10.375
9.5
8.75
12
12
12
11.5
16
12.5
12.25
2.625
3.125
3.125
2
3.75
2.8125
3.25
2.625
5
5
5
3.25
3
5
4.875
5
2
12
5
d
w
d
d
cnt
6.5
1
6.5
1
39
39
39
6.25
0.9375
0.9375
1
1
1
39
0.9375
1
2 39
5.75
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
total
36
sq ft
6.20
4.26
3.96
2.79
2.96
4.44
4.16
6.20
2.50
2.12
1.99
1.49
1.60
1.99
1.99
2.20
2.57
2.38
1.57
1.02
0.74
1.73
2.34
2.52
2.50
2.34
1.63
0.68
1.53
2.23
2.39
0.00
1.89
1.99
1.93
1.28
1.46
1.81
2.05
1.89
6.14
4.70
4.70
2.87
2.83
4.55
4.35
cu ft
74.46
51.06
47.58
33.52
35.58
53.33
49.91
74.46
30.06
25.45
23.83
17.91
19.17
23.83
23.83
26.43
30.81
28.58
18.86
12.22
8.85
20.73
28.10
30.22
30.00
28.10
19.54
8.16
18.31
26.81
28.69
0.00
22.64
23.83
23.21
15.33
17.51
21.74
24.65
22.64
73.65
56.38
56.38
34.40
34.00
54.63
52.20
tons
18.24
12.51
11.66
8.21
8.72
13.07
12.23
18.24
7.36
6.24
5.84
4.39
4.70
5.84
5.84
6.48
7.55
7.00
4.62
2.99
2.17
5.08
6.89
7.40
7.35
6.89
4.79
2.00
4.49
6.57
7.03
0.00
5.55
5.84
5.69
3.76
4.29
5.33
6.04
5.55
18.04
13.81
13.81
8.43
8.33
13.38
12.79
6.00
72.02
17.65
129.47
1553.60
380.63
Table 19: (continued) Core column data for selected floors
floor 002-007
col
w
d
cnt
w
d
cnt w
d
cnt
501
52
5
2
12
5
2 39
6.5
1
502
52
4.75
2
12.5
4.75
2
503
52
4.375
2
13.25
4.375
2
504
52 2.9375
2 16.125 2.9375
2
505
52
3.5
2
11
3.5
2
506
52
4.875
2
12.26
4.875
2
507
52
4.625
2
12.75
4.625
2
508
52
5
2
12
5
2 39
6.5
1
601
43
4.5
2
5
4.5
2
602
36
4.5
2
7
4.5
2
603
36
4.25
2
7.5
4.25
2
604
36 3.1875
2
7.625 3.1875
2
605
36 3.4375
2
7.125 3.4375
2
606
36
4.25
2
7.5
4.25
2
607
36
4.25
2
7.5
4.25
2
608
43
4
2
6
4
2
701
37
4.5
2
6
4.5
2
702
30
4.5
2
17
4.5
2
703
34
3.375
2
9.25
3.375
2
704 12.58
2.02
1
16.8
3.21
2
705
28
2.125
2
12.75
2.125
2
706
30
4.375
2
8.25
4.375
2
707
30
4.5
2
17
4.5
2
708
37
4.625
2
5.75
4.625
2
801
34
5
2
5
5
2
802
30
4.5
2
17
4.5
2
803
34
4
2
7
4
2
804
28
3
1
11
3
2
805
34
3.125
2
10.75
3.125
2
806
30
4.375
2
17.25
4.375
2
807
34
4.875
2
5.25
4.875
2
808
901
43
4
2
6
4
2
902
36
4.125
2
7.75
4.125
2
903
36
4.125
2
7.75
4.125
2
904
36
2.875
2
6.25
2.875
2
905
22
5
2
4
5
2
906
36
4.125
2
7.75
4.125
2
907
36
4.5
2
7
4.5
2
908
43
4
2
6
4
2
1001
52
5
2
12
5
2 39
6.5
1
1002
52
5
2
12
5
2 39
1.25
1
1003
52
5
2
12
5
2 39
1.25
1
1004
52
3.25
2
11.5
3.25
2
1005
52
3.125
2
15.75
3.125
2
1006
52
5
2
12
5
2 39 0.9375
1
1007
52
4.875
2
12.25
4.875
2
1008
52
5
2
12
5
2 39
6.5
total
1
sq ft
6.20
4.26
3.96
2.78
3.06
4.35
4.16
6.20
3.00
2.69
2.57
1.93
2.06
2.57
2.57
2.72
2.69
2.94
2.03
0.93
1.20
2.32
2.94
2.75
2.71
2.94
2.28
1.04
1.94
2.87
2.66
0.00
2.72
2.51
2.51
1.69
1.81
2.51
2.69
2.72
6.20
4.78
4.78
2.87
2.94
4.70
4.35
6.20
145.28
37
cu ft
74.46
51.06
47.58
33.35
36.75
52.21
49.91
74.46
36.00
32.25
30.81
23.18
24.71
30.81
30.81
32.67
32.25
35.25
24.33
11.11
14.43
27.89
35.25
32.95
32.50
35.25
27.33
12.50
23.31
34.45
31.89
0.00
32.67
30.08
30.08
20.24
21.67
30.08
32.25
32.67
74.46
57.40
57.40
34.40
35.29
56.38
52.20
tons
18.24
12.51
11.66
8.17
9.00
12.79
12.23
18.24
8.82
7.90
7.55
5.68
6.05
7.55
7.55
8.00
7.90
8.64
5.96
2.72
3.54
6.83
8.64
8.07
7.96
8.64
6.70
3.06
5.71
8.44
7.81
0.00
8.00
7.37
7.37
4.96
5.31
7.37
7.90
8.00
18.24
14.06
14.06
8.43
8.65
13.81
12.79
74.46
18.24
1743.42 427.14
Table 19: (continued) Core column data for selected floors
col
501
502
503
504
505
506
507
508
601
602
603
604
605
606
607
608
701
702
703
704
705
706
707
708
801
802
803
804
805
806
807
808
901
902
903
904
905
906
907
908
1001
1002
1003
1004
1005
1006
1007
1008
w
floor 51-53
d
cnt w d cnt
3.25
2
3.125
2
2
2
1.4375
2
1.5625
2
2.1875
2
2.0525
2
3.25
2
1.4375
2
1.5625
2
1.4375
2
1.1275
2
1.1875
2
1.6875
2
1.5
2
1.125
2
1.6875
2
3.82
2
1.125
2
1.128
2
1.063
2
2.843
2
3.82
2
1.6875
2
1.8125
2
3.82
2
1.8125
2
1.936
2
2.468
2
3.82
2
1.6875
2
52
52
52
52
52
52
52
52
43
36
36
36
36
36
36
43
37
12.56
34
12.624
12.624
12.624
12.56
37
34
12.56
34
12.624
12.624
12.56
34
d
cnt
3.25
2
2.0625
2
1.9375
2
1.4375
2
1.5625
2
2.125
2
2
2
3.25
2
1.4375
2
1.5625
2
1.4375
2
1.1275
2
1.1875
2
1.625
2
1.5
2
1.125
2
1.6875
2
2.38
1
1.125
2
0.695
1
0.68
1
1.77
1
2.38
1
1.6875
2
1.8125
2
2.38
1
1.8125
2
1.205
1
1.545
1
2.38
1
1.6875
2
w
15.5
17.875
18.175
19.125
14.875
17.75
18
15.5
11.125
12.875
13.125
11.75
11.625
12.75
12
11.75
11.625
17.2
13.75
15.515
15.5
16.59
17.2
11.625
11.375
17.2
11.375
16.025
16.385
17.2
11.625
22
12.58
36
36
22
12.58
12.6
12.624
52
43
43
52
52
43
43
2.0325
2.02
1.4375
0.875
1.4375
2.02
2.19
1.77
3.125
2.25
2.8125
1.375
1.25
2.625
2.25
2
1
2
2
2
1
1
1
2
2
2
2
2
2
2
8.875
16.8
13.125
12.25
11.125
16.8
17
16.59
15.55
17.6
16.375
15.25
19.5
16.75
17.5
2.0625
3.21
1.4375
0.675
1.4375
3.21
3.5
2.843
3.125
2.25
2.8125
1.4375
1.3125
2.625
2.3125
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
52
3.125
2
15.75
3.125
2
total
38
sq ft
3.05
2.27
1.90
1.42
1.45
2.07
1.96
3.05
1.08
1.06
0.98
0.75
0.79
1.11
1.00
0.86
1.14
1.12
0.75
0.30
0.29
0.81
1.12
1.14
1.14
1.12
1.14
0.54
0.70
1.12
1.07
0.00
0.88
0.93
0.98
0.55
0.66
0.93
1.02
0.81
2.93
1.89
2.32
1.30
1.26
2.18
1.91
cu ft
36.56
27.18
22.85
17.04
17.42
24.89
23.49
36.56
12.97
12.73
11.77
8.97
9.43
13.34
12.00
10.27
13.68
13.44
8.95
3.65
3.46
9.72
13.44
13.68
13.71
13.44
13.71
6.44
8.37
13.44
12.83
0.00
10.50
11.11
11.77
6.63
7.94
11.11
12.22
9.72
35.18
22.73
27.83
15.57
15.10
26.14
22.87
tons
8.96
6.66
5.60
4.17
4.27
6.10
5.76
8.96
3.18
3.12
2.88
2.20
2.31
3.27
2.94
2.52
3.35
3.29
2.19
0.89
0.85
2.38
3.29
3.35
3.36
3.29
3.36
1.58
2.05
3.29
3.14
0.00
2.57
2.72
2.88
1.62
1.94
2.72
2.99
2.38
8.62
5.57
6.82
3.81
3.70
6.40
5.60
2.94
35.29
8.65
61.76
741.11
181.57
Table 19: (continued) Core column data for selected floors
col
501
502
503
504
505
506
507
508
601
602
603
604
605
606
607
608
701
702
703
704
705
706
707
708
801
802
803
804
805
806
807
808
901
902
903
904
905
906
907
908
1001
1002
1003
1004
1005
1006
1007
w
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
10.908
12.624
12.624
10.908
10.908
12.624
12.624
10.908
10.908
12.624
12.624
12.624
12.624
12.624
12.624
10.908
10.908
12.624
10.908
10.908
12.624
12.624
12.624
d
cnt
0.98
1
0.73
1
0.695
1
0.57
1
0.68
1
0.695
1
0.68
1
0.98
1
0.39
1
0.42
1
0.451
1
0.345
1
0.39
1
0.451
1
0.451
1
0.39
1
0.58
1
0.465
1
0.338
1
0.308
1
0.308
1
0.418
1
0.54
1
0.755
1
0.59
1
0.465
1
0.39
1
0.284
1
0.45
1
0.54
1
0.465
1
floor 105-106
w
d
cnt w d cnt
15.8 1.563
2
15.55 1.188
2
15.515 1.128
2
14.65 0.938
2
14.74 1.063
2
15.515 1.128
2
14.74 1.063
2
15.8 1.563
2
12 0.606
2
11.5 0.686
2
12.023 0.778
2
10 0.576
2
12 0.606
2
12.023 0.778
2
12.023 0.778
2
12 0.606
2
12.19 0.921
2
14.545 0.748
2
8.031 0.592
2
8 0.526
2
8 0.526
2
10.04 0.716
2
14.62 0.673
2
12.365 1.236
2
12.19 0.921
2
14.545 0.748
2
12 0.606
2
8 0.515
2
10.072 0.783
2
14.62 0.673
2
14.545 0.748
2
10.908
12.624
12.624
14
10.908
12.624
12.624
10.908
12.624
12.624
12.624
12.624
12.624
12.624
12.624
0.43
0.451
0.57
0.375
0.345
0.451
0.465
0.43
1.09
1.045
0.89
0.68
0.61
0.68
0.695
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
12.04
12.023
14.65
10
10
12.023
14.545
12.04
16.13
15.81
15.71
14.74
14.69
14.74
15.515
0.671
0.778
0.938
0.375
0.576
0.778
0.748
0.671
2.093
1.748
1.438
1.063
0.998
1.063
1.128
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1008
12.624
1.09
1
16.13
2.093
2
total
39
sq ft
0.43
0.32
0.30
0.24
0.28
0.30
0.28
0.43
0.13
0.15
0.17
0.11
0.13
0.17
0.17
0.13
0.20
0.19
0.10
0.09
0.09
0.14
0.18
0.27
0.20
0.19
0.13
0.08
0.15
0.18
0.19
0.00
0.14
0.17
0.24
0.13
0.11
0.17
0.19
0.14
0.56
0.48
0.39
0.28
0.26
0.28
0.30
cu ft
5.15
3.85
3.65
2.89
3.33
3.65
3.33
5.15
1.57
1.76
2.03
1.27
1.57
2.03
2.03
1.57
2.40
2.30
1.15
1.03
1.03
1.64
2.21
3.23
2.41
2.30
1.57
0.94
1.79
2.21
2.30
0.00
1.74
2.03
2.89
1.50
1.27
2.03
2.30
1.74
6.77
5.71
4.70
3.33
3.09
3.33
3.65
tons
1.26
0.94
0.89
0.71
0.82
0.89
0.82
1.26
0.38
0.43
0.50
0.31
0.38
0.50
0.50
0.38
0.59
0.56
0.28
0.25
0.25
0.40
0.54
0.79
0.59
0.56
0.38
0.23
0.44
0.54
0.56
0.00
0.43
0.50
0.71
0.37
0.31
0.50
0.56
0.43
1.66
1.40
1.15
0.82
0.76
0.82
0.89
0.56
6.77
1.66
10.51
126.16
30.91
Table 19: (continued) Core column data for selected floors
d
cnt
0.84
1
0.73
1
0.73
1
0.73
1
0.73
1
0.73
1
0.73
1
0.84
1
0.62
1
0.61
1
0.61
1
0.71
1
0.61
1
0.61
1
0.61
1
0.62
1
0.755
1
0.61
1
0.46
1
0.308
1
0.308
1
0.46
1
0.61
1
0.73
1
0.755
1
0.61
1
0.47
1
0.294
1
0.42
1
0.61
1
0.68
1
w
15.68
15.55
15.55
15.55
15.55
15.55
15.55
15.68
12.23
14.59
14.59
12.23
14.59
14.59
14.59
12.23
12.365
14.59
10.072
8
8
10.072
14.59
15.55
12.365
14.59
12.08
8
14.5
14.59
14.74
floor 107
d
cnt w d cnt
1.378
2
1.188
2
1.188
2
1.188
2
1.188
2
1.188
2
1.188
2
1.378
2
0.866
2
0.998
2
0.998
2
1.106
2
0.998
2
0.998
2
0.998
2
0.866
2
1.236
2
0.998
2
0.783
2
0.528
2
0.528
2
0.783
2
0.998
2
1.188
2
1.236
2
0.998
2
0.736
2
0.516
2
0.686
2
0.998
2
1.063
2
col
501
502
503
504
505
506
507
508
601
602
603
604
605
606
607
608
701
702
703
704
705
706
707
708
801
802
803
804
805
806
807
808
901
902
903
904
905
906
907
908
1001
1002
1003
1004
1005
1006
1007
w
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
10.908
12.624
12.624
10.908
12.624
12.624
12.624
10.908
10.908
12.624
12.624
12.624
12.624
12.624
12.624
12.624
10.908
12.624
10.908
10.908
12.624
12.624
12.624
10.908
12.624
10.908
10.908
10.908
12.624
12.624
10.908
12.624
12.624
12.624
12.624
12.624
12.624
12.624
0.62
0.61
0.71
0.71
0.71
0.61
0.61
0.62
0.84
0.73
0.73
0.73
0.73
0.73
0.73
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
12.23
14.59
12.32
12.32
12.32
14.59
14.59
12.23
15.68
15.55
15.55
15.55
15.55
15.55
15.55
0.866
0.998
1.106
1.106
1.106
0.998
0.998
0.866
1.378
1.188
1.188
1.188
1.188
1.188
1.188
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1008
12.624
0.84
1
15.68
1.378
2
total
40
sq ft
0.37
0.32
0.32
0.32
0.32
0.32
0.32
0.37
0.19
0.26
0.26
0.24
0.26
0.26
0.26
0.19
0.27
0.26
0.15
0.09
0.09
0.15
0.26
0.32
0.27
0.26
0.16
0.08
0.17
0.26
0.28
0.00
0.19
0.26
0.24
0.24
0.24
0.26
0.26
0.19
0.37
0.32
0.32
0.32
0.32
0.32
0.32
cu ft
4.48
3.85
3.85
3.85
3.85
3.85
3.85
4.48
2.33
3.07
3.07
2.90
3.07
3.07
3.07
2.33
3.23
3.07
1.80
1.03
1.03
1.80
3.07
3.85
3.23
3.07
1.91
0.96
2.10
3.07
3.33
0.00
2.33
3.07
2.92
2.92
2.92
3.07
3.07
2.33
4.48
3.85
3.85
3.85
3.85
3.85
3.85
tons
1.10
0.94
0.94
0.94
0.94
0.94
0.94
1.10
0.57
0.75
0.75
0.71
0.75
0.75
0.75
0.57
0.79
0.75
0.44
0.25
0.25
0.44
0.75
0.94
0.79
0.75
0.47
0.23
0.51
0.75
0.82
0.00
0.57
0.75
0.71
0.71
0.71
0.75
0.75
0.57
1.10
0.94
0.94
0.94
0.94
0.94
0.94
0.37
4.48
1.10
12.18
146.15
35.81
Table 19: (continued) Core column data for selected floors
floor 108
d
cnt w d cnt
1.813
2
1.188
2
1.188
2
1.188
2
1.188
2
1.188
2
1.188
2
1.813
2
0.998
2
0.998
2
0.998
2
0.998
2
0.998
2
0.998
2
0.998
2
0.998
2
1.813
2
1.188
2
0.783
2
1.188
2
0.528
2
0.783
2
1.188
2
0.783
2
1.813
2
1.188
2
0.736
2
col
501
502
503
504
505
506
507
508
601
602
603
604
605
606
607
608
701
702
703
704
705
706
707
708
801
802
803
804
805
806
807
808
901
902
903
904
905
906
907
908
1001
1002
1003
1004
1005
1006
1007
w
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
10.908
d
cnt
1.125
1
0.73
1
0.73
1
0.73
1
0.73
1
0.73
1
0.73
1
1.125
1
0.61
1
0.61
1
0.61
1
0.61
1
0.61
1
0.61
1
0.61
1
0.61
1
1.125
1
0.73
1
0.46
1
0.73
1
0.308
1
0.46
1
0.73
1
0.46
1
1.125
1
0.73
1
0.47
1
w
16.945
15.55
15.55
15.55
15.55
15.55
15.55
16.945
14.59
14.59
14.59
14.59
14.59
14.59
14.59
14.59
16.945
15.55
10.072
15.55
8
10.072
15.55
10.072
16.945
15.55
12.08
12.624
12.624
12.624
0.42
0.73
1.125
1
1
1
14.5
15.55
16.945
0.686
1.188
1.813
2
2
2
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61
1.125
0.73
0.73
0.73
0.73
0.73
0.73
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
14.59
14.59
14.59
14.59
14.59
14.59
14.59
14.59
16.945
15.55
15.55
15.55
15.55
15.55
15.55
0.998
0.998
0.998
0.998
0.998
0.998
0.998
0.998
1.813
1.188
1.188
1.188
1.188
1.188
1.188
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1008
12.624
1.125
1
16.945
1.813
2
total
41
sq ft
0.53
0.32
0.32
0.32
0.32
0.32
0.32
0.53
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.53
0.32
0.15
0.32
0.09
0.15
0.32
0.15
0.53
0.32
0.16
0.00
0.17
0.32
0.53
0.00
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.53
0.32
0.32
0.32
0.32
0.32
0.32
cu ft
6.30
3.85
3.85
3.85
3.85
3.85
3.85
6.30
3.07
3.07
3.07
3.07
3.07
3.07
3.07
3.07
6.30
3.85
1.80
3.85
1.03
1.80
3.85
1.80
6.30
3.85
1.91
0.00
2.10
3.85
6.30
0.00
3.07
3.07
3.07
3.07
3.07
3.07
3.07
3.07
6.30
3.85
3.85
3.85
3.85
3.85
3.85
tons
1.54
0.94
0.94
0.94
0.94
0.94
0.94
1.54
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
1.54
0.94
0.44
0.94
0.25
0.44
0.94
0.44
1.54
0.94
0.47
0.00
0.51
0.94
1.54
0.00
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
1.54
0.94
0.94
0.94
0.94
0.94
0.94
0.53
6.30
1.54
14.09
169.05
41.42
Table 19: (continued) Core column data for selected floors
floor 109-110
d
cnt w d cnt
1.188
2
1.188
2
1.188
2
1.188
2
1.188
2
1.188
2
1.188
2
1.188
2
0.998
2
0.998
2
0.998
2
0.998
2
0.998
2
0.998
2
0.998
2
0.998
2
1.188
2
1.188
2
0.593
2
1.188
2
1.188
2
0.643
2
1.188
2
col
501
502
503
504
505
506
507
508
601
602
603
604
605
606
607
608
701
702
703
704
705
706
707
708
801
802
803
804
805
806
807
808
901
902
903
904
905
906
907
908
1001
1002
1003
1004
1005
1006
1007
w
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
d
cnt
0.73
1
0.73
1
0.73
1
0.73
1
0.73
1
0.73
1
0.73
1
0.73
1
0.61
1
0.61
1
0.61
1
0.61
1
0.61
1
0.61
1
0.61
1
0.61
1
0.73
1
0.73
1
0.339
1
0.73
1
0.73
1
0.378
1
0.73
1
w
15.55
15.55
15.55
15.55
15.55
15.55
15.55
15.55
14.59
14.59
14.59
14.59
14.59
14.59
14.59
14.59
15.55
15.55
8.31
15.55
15.55
10
15.55
12.624
12.624
12.624
0.73
0.73
0.371
1
1
1
15.55
15.55
8.077
1.188
1.188
0.641
2
2
2
12.624
12.624
12.624
0.42
0.73
0.73
1
1
1
11.5
15.55
15.55
0.686
1.188
1.188
2
2
2
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.73
0.73
0.73
0.73
0.73
0.73
0.73
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
14.59
14.59
14.59
14.59
14.59
14.59
14.59
14.59
15.55
15.55
15.55
15.55
15.55
15.55
15.55
0.998
0.998
0.998
0.998
0.998
0.998
0.998
0.998
1.188
1.188
1.188
1.188
1.188
1.188
1.188
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1008
12.624
0.73
1
15.55
1.188
2
total
42
sq ft
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.32
0.32
0.10
0.32
0.32
0.12
0.32
0.00
0.32
0.32
0.10
0.00
0.15
0.32
0.32
0.00
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.32
0.32
0.32
0.32
0.32
0.32
0.32
cu ft
3.85
3.85
3.85
3.85
3.85
3.85
3.85
3.85
3.07
3.07
3.07
3.07
3.07
3.07
3.07
3.07
3.85
3.85
1.18
3.85
3.85
1.47
3.85
0.00
3.85
3.85
1.25
0.00
1.76
3.85
3.85
0.00
3.07
3.07
3.07
3.07
3.07
3.07
3.07
3.07
3.85
3.85
3.85
3.85
3.85
3.85
3.85
tons
0.94
0.94
0.94
0.94
0.94
0.94
0.94
0.94
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.94
0.94
0.29
0.94
0.94
0.36
0.94
0.00
0.94
0.94
0.31
0.00
0.43
0.94
0.94
0.00
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.94
0.94
0.94
0.94
0.94
0.94
0.94
0.32
3.85
0.94
12.18
146.15
35.81
Table 19: (continued) Core column data for selected floors
floor 111 (roof)
w
d
cnt w d cnt
10.072 0.783
2
15.55 1.188
2
15.55 1.188
2
15.55 1.188
2
15.55 1.188
2
15.55 1.188
2
15.55 1.188
2
10.072 0.783
2
14.59 0.998
2
14.59 0.998
2
14.59 0.998
2
14.59 0.998
2
14.59 0.998
2
14.59 0.998
2
14.59 0.998
2
14.59 0.998
2
10.072 0.783
2
15.55 1.188
2
col
501
502
503
504
505
506
507
508
601
602
603
604
605
606
607
608
701
702
703
704
705
706
707
708
801
802
803
804
805
806
807
808
901
902
903
904
905
906
907
908
1001
1002
1003
1004
1005
1006
1007
w
10.908
12.624
12.624
12.624
12.624
12.624
12.624
10.908
12.624
12.624
12.624
12.624
12.624
12.624
12.624
12.624
10.908
12.624
d
cnt
0.45
1
0.73
1
0.73
1
0.73
1
0.73
1
0.73
1
0.73
1
0.45
1
0.61
1
0.61
1
0.61
1
0.61
1
0.61
1
0.61
1
0.61
1
0.61
1
0.45
1
0.73
1
12.624
12.624
0.73
0.73
1
1
15.55
15.55
1.188
1.188
2
2
12.624
0.73
1
15.55
1.188
2
10.908
12.624
0.45
0.73
1
1
10.072
15.55
0.783
1.188
2
2
10.908
12.624
0.45
0.73
1
1
10.072
15.55
0.783
1.188
2
2
12.624
0.61
1
14.59
0.998
2
12.624
12.624
12.624
12.624
12.624
12.624
10.908
12.624
12.624
12.624
12.624
12.624
12.624
0.61
0.61
0.61
0.61
0.61
0.61
0.45
0.73
0.73
0.73
0.73
0.73
0.73
1
1
1
1
1
1
1
1
1
1
1
1
1
14.59
14.59
14.59
14.59
14.59
14.59
10.072
15.55
15.55
15.55
15.55
15.55
15.55
0.998
0.998
0.998
0.998
0.998
0.998
0.783
1.188
1.188
1.188
1.188
1.188
1.188
2
2
2
2
2
2
2
2
2
2
2
2
2
1008
10.908
0.45
1
10.072
0.783
2
total
43
sq ft
0.14
0.32
0.32
0.32
0.32
0.32
0.32
0.14
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.14
0.32
0.00
0.32
0.32
0.00
0.32
0.00
0.14
0.32
0.00
0.00
0.00
0.14
0.32
0.00
0.26
0.00
0.26
0.26
0.26
0.26
0.26
0.26
0.14
0.32
0.32
0.32
0.32
0.32
0.32
cu ft
1.72
3.85
3.85
3.85
3.85
3.85
3.85
1.72
3.07
3.07
3.07
3.07
3.07
3.07
3.07
3.07
1.72
3.85
0.00
3.85
3.85
0.00
3.85
0.00
1.72
3.85
0.00
0.00
0.00
1.72
3.85
0.00
3.07
0.00
3.07
3.07
3.07
3.07
3.07
3.07
1.72
3.85
3.85
3.85
3.85
3.85
3.85
tons
0.42
0.94
0.94
0.94
0.94
0.94
0.94
0.42
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.42
0.94
0.00
0.94
0.94
0.00
0.94
0.00
0.42
0.94
0.00
0.00
0.00
0.42
0.94
0.00
0.75
0.00
0.75
0.75
0.75
0.75
0.75
0.75
0.42
0.94
0.94
0.94
0.94
0.94
0.94
0.14
1.72
0.42
10.61
127.34
31.20

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